The Humboldt Penguin (Spheniscus humboldti) Rete Tibiotarsale – A supreme biological heat exchanger

Journal of Thermal Biology 67 (2017) 67–78

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The Humboldt Penguin (Spheniscus humboldti) Rete Tibiotarsale – A supreme biological heat exchanger Shaked Kazasa,1, Moran Benellya,1, Saar Golanb,c,a, a b c

MARK

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Faculty of Biomedical Engineering, Technion – Israel Institute of Technology, Israel Department of Chemical Engineering, Ariel University, Israel Department of Mechanical Engineering, Ariel University, Israel

A R T I C L E I N F O

A B S T R A C T

Keywords: Biological heat exchanger Thermal endurance Physiological adaptation Finite elements

Humans are unable to survive low temperature environments without custom designed clothing and support systems. In contrast, certain penguin species inhabit extremely cold climates without losing substantial energy to self-heating (emperor penguins ambient temperature plummets to as low as −45 °C). Penguins accomplish this task by relying on distinct anatomical, physiological and behavioral adaptations. One such adaptation is a blood vessel heat exchanger called the ‘Rete Tibiotarsale’ – an intermingled network of arteries and veins found in penguins’ legs. The Rete existence results in blood occupying the foot expressing a lower average temperature and thus the penguin loosing less heat to the ground. This study examines the Rete significance for the species thermal endurance. The penguin anatomy (leg and main blood vessels) is reconstructed using data chiefly based on the Humboldt species. The resulting model is thermally analyzed using finite element (COMSOL) with the species environment used as boundary conditions. A human-like blood vessel configuration, scaled to the penguin's dimensions, is used as a control for the study. Results indicate that the Rete existence facilitates upkeep of 25 − 65% of the species total metabolic energy production as compared with the human-like configuration; thus making the Rete probably crucial for penguin thermal endurance. Here, we quantitatively link for the first time the function and structure of this remarkable physiological phenotype.

1. Introduction Certain penguin species inhabit extremely cold climates without freezing or losing excessive energy to self-heating (emperor penguins ambient temperature plummets to as low as −45 °C). Penguins are able to survive harsh cold climate due to specialized anatomical, physiological and behavioral adaptations for minimizing heat loss (Pinshow et al., 1975; Gilbert et al., 2008; Chappell et al., 1989; Stahel and Nicol, 1982; Cherel et al., 1993; Cherel, 1995; Portugal and Guillemette, 2011; McCafferty et al., 2013). One such adaptation is an intermingled network of arteries and veins at the distal part of the penguin leg (above the foot), known as the Rete Tibiotarsale (RT), that forms a biological heat exchanger (Frost et al., 1975; Midtgård, 1981). This heat exchanger employs hot arterial blood flowing to the foot to heat cold venous blood flowing back to the body. The end result of this adaptation is the foot expressing an average lower temperature and thus the penguin loosing significantly less heat to the ground (Drent and Stonehouse, 1971). Configuration 1 of Fig. 1b schematically illustrates an arrangement

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1

of blood vessels with similar to human anatomy in terms of vessels dimensions and positions inside the penguin limb (as if scaled from a human leg). Configuration 2 of Fig. 1b illustrates the actual penguin blood vessel organization. Here, entwined blood vessels form a biological heat exchanger. The heat exchanger phenotype is present in numerous species and in various formations (Midtgård, 1981). It is not limited to the lower limbs of birds. Similar formations are found in the dog and cat paw pads, the Saanen goat brain and in the mallard's tongue and eyes (Ninomiya et al., 2013; Atalgin, 2011; Midtgård, 1984). Numerous questions can be raised regarding the heat exchanger advantages: How efficient is it? How do the blood vessels develop during the animal growth? Do they form together and then differentiate into arteries and veins or does motion of formerly otherwise arranged vessels take place? And so forth. This study aims to characterize the RT contribution to the penguin thermal (energetic) endurance.

Corresponding author at: Department of Chemical Engineering, Room 6.0.3, Ariel University, P.O.B. 3, Ariel 40700, Israel. E-mail address: [email protected] (S. Golan). Equal contributors.

http://dx.doi.org/10.1016/j.jtherbio.2017.04.011 Received 7 June 2016; Received in revised form 7 April 2017; Accepted 28 April 2017 Available online 04 May 2017 0306-4565/ © 2017 Elsevier Ltd. All rights reserved.

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Fig. 1. Penguin model. (a) Image of a Humboldt penguin depicting the leg anatomy (Wikipedia). Superimposed are some of the model parameters. (b) Schematic illustration of two blood vessels arrangements/configurations. 1 – Human (like) configuration. 2 – The actual (penguin) entwined or heat exchanger configuration. (c) Bone structure of the Rockhopper penguin (Website). Tarsometatarsus bones are indicated by red arrows. (d) Image of a penguin foot illustrating the remaining model parameters (courtesy of Rotem Guzman and Dr. Gillad Goldstein of the Tel Aviv - Ramat Gan Zoological Center). (e) The Humboldt penguin blood vessels. Anterior view of the intertarsal joint at the left leg base. lm – lateral metatarsal vein, mm – medial metatarsal vein (Midtgård, 1981). Dotted and thin horizontal superimposed lines represent distances of main arteries and peripheral veins from the leg exterior, respectively. Vertical measurement represents the heat exchanger length. Dimensions are in mm. Measurements are inferred from the full horizontal line representing the leg diameter (25.7 mm). Veins are marked black. Arteries are marked gray. (f) Steps in the evolution of heat exchanger systems in the hind limb of birds (Midtgård, 1981). The stage representing a superior view of a cross section of the Humboldt penguin Rete is encircled and enlarged in the inset. Veins are marked black. Arteries are marked white. (g) Vasculature of half a leg as obtained from a Humboldt penguin leg cast (cross sectioned) is presented as semitransparent background (Midtgård, 1981). Vessels dimensions are evaluated using image processing (Siemens NX 10) and are superimposed with the respective vessel category listed in the legend to the left. Vessels are idealized as cylindrical (circular cross section) and diameter averaged (see text). Arteries are marked red. Veins are marked blue. Measurements are inferred from the scale bar (bottom right). (h) The penguin leg model. Insets show a region of the Rete and the corresponding blood vessels. Arteries are marked red. Veins are marked blue. (i) FEA model. A very fine mesh is applied within and about each vessel. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

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9

1.1. Anatomy

8

RT is documented in numerous penguin species – Emperor (Aptenodytes forsteri), Adelie (Pygoscelis adeliae), King (Aptenodytes patagonicus), Rockhopper (Eudyptes chrysocome), Yellow-eyed (Megadyptes antipodes) and Macaroni (Eudyptes chrysolophus) (Midtgård, 1981; Trawa, 1970; Filhol, 1882; Desboefs, 1966). Its anatomy has been documented in relatively more detail in the Humboldt penguin (Spheniscus humboldti) (Midtgård, 1981). Therefore, this species was specifically targeted for investigation. Penguin species weigh from ~1 kg up to ~38 kg (values are gender averaged) (Davis). The Humboldt penguin has an average weight of ~4.7 kg. Some Supporting data for the RT model was adopted from the YellowEyed penguin (average weight ~5.5 kg) and the Rockhopper penguin (average weight ~2.5 kg), the latter confined to presenting bone anatomy. As control for the study, we employed a human like configuration (Fig. 1b, configuration 1) – an arrangement of blood vessels with similar to human anatomy in terms of vessels dimensions and positions inside the penguin limb (as if scaled from a human leg). Here, in contrast with the lack in penguin leg data, sections of the human leg are available in abundance (Faure and Merloz, 1987; Borley et al., 2008; Netter, 2014; Rohen et al., 2015). Even a rudimentary investigation reveals that most human veins are superficial and located about the leg periphery. Intuitively, such a formation is less efficient in terms of heat preservation compared with the penguin RT (Fig. 1b, configuration 2).

Value [cm]

7 6 5 8.08

4 7.06

7.02

6.61

3 2 2.83

2.57

1

1.26

0 Leg Length Leg Perimeter Leg Diameter Anterior foot Posterior foot Foot Length width width

Foot tissue width

Fig. 2. Humboldt penguin dimensions. The model dimensional parameters are provided. Average values are listed inside the bars. Error bars indicate the standard deviations of 5 animals (9 legs). Variations from the average values are relatively small (below 9%).

2.1.2. Geometric model The leg was modeled as a cylinder (Fig. 1h). The ankle was modeled as an inclined cylinder having the same diameter as that of the leg (Fig. 1h). The sole was conservatively assumed to make full contact with the ground (no contact resistance) and was thus modeled as a trapezoid prism neglecting the nails and using the middle finger length as reference (Fig. 1h).

2.1.3. Blood vessels Midtgård details the Humboldt penguin leg vasculature (Midtgård, 1981). There are two main arteries of similar size – the medial and lateral branches of the cranial tibial artery. In contrast, the foot is drained by numerous veins of two types: the medial and lateral metatarsal superficial veins that are not in intimate contact with arteries and are relatively small and the deeply situated veins forming counter current heat exchangers with the arteries. The total number of arteries and veins is on average 6 (not including the two main arteries) and 17, respectively – see Figs. 1e-g. The vasculature of half a leg, as obtained from a Humboldt penguin leg cast (cross section), is presented in Fig. 1g at the background. It consists of: one large artery, three small arteries, two large veins, and six small veins. The superficial vein is not shown (see Fig. 1e). The vessels dimensions were evaluated by image processing as ellipses or circles (if ellipse axes lengths differed by less than 10%) and are superimposed on the anatomical cross section. All vessels were modeled as cylindrical (circular cross section). A vessel having an elliptic cross section was given a diameter value inferred from two circles having the same area and perimeter (averaged). The model employed the blood vessels actual cross sectional centers. The vessels diameters were averaged according to two categories – artery/vein and large/small, thus resulting in a total of four vessel types: small vein (96 µm), large vein (204 µm), small artery (103 µm) and large artery (538 µm). The superficial veins are not visible in the cross section. However, as it was stated that these veins are relatively small, we estimated their diameter as the small veins average (96 µm). Each vessel category is detailed in the legend to the left of Fig. 1g. The vasculature was idealized as sagittally symmetric – i.e., the distance between the leg center and each main artery was assumed similar (Fig. 1h). Thus, it was sufficient to model only half a leg (Fig. 1i). Thermal environmental differences between the medial and

1.2. Environment Two distinct habitats were employed in order to evaluate the thermal environment effects: 1. A Humboldt species captivity habitat at Stanley Park Zoo, Vancouver (Canada). This habitat was used as the main reference since climate was well documented and coupled to thermistor based measurements at three positions on the penguin body – deep in the gullet, the skin on the back beneath the feathers and the foot (Drent and Stonehouse, 1971). 2. The Emperor species habitat at the breeding colony in Antarctica was employed as reference for very harsh thermal conditions (McCafferty et al., 2013).

2. Methods 2.1. Model 2.1.1. Geometric dimensions Figs. 1a and c-d present the Humboldt penguin leg and foot geometric parameters used in the study. Table 1 and Fig. 2 summarize their values. All data is provided courtesy of the Hai Park Zoo (Mozkin, Israel). Ankle dimensions were based on the Tarsometatarsus bone. This bone links the foot and leg but does not contact the ground (Figs. 1c-d) (James and Olson, 1949). The Tarsometatarsus length was assumed identical to that of the Yellow–Eyed penguin – 35.5 mm (Livezey, 1989).

Table 1 Humboldt penguin dimensions (nanimals=5, nlegs=9, all dimensions are in cm, data is provided courtesy of the Hai Park Zoo, Mozkin, Israel).

Average STD Normalized STD [%]

Leg length

Leg perimeter

Leg diameter

Anterior foot width

Posterior foot width

Foot length

Foot tissue width

7.06 0.50 7.04

8.08 0.48 5.89

2.57 0.15 5.89

7.02 0.56 7.99

2.83 0.24 8.32

6.61 0.57 8.57

1.26 0.07 5.46

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Fig. 3. Human model. (a) Cross Section (#D7) of the human leg as made just distal to the middle of the tibial diaphysis (Faure and Merloz, 1987). (b) The cross section position in the human leg is marked by red arrows (Faure and Merloz, 1987). (c) The human cross section and corresponding blood vessels were scaled to the penguin dimensions (dotted line, diameter 25.7 mm) in order to create the human control configuration (Faure and Merloz, 1987). Scaling was performed using a CAD program (Siemens NX 10). (d) The human finite element model (COMSOL). A very fine mesh is applied inside and about each vessel. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

standing undisturbed (upright position) when at rest and three minutes following recovery from a free roaming exercise on land (running on foot and tobogganing), respectively. We take a representative flow rate as the average of resting and shortly following mild excersize recovery – (24+59)/2=41.5 ml/min (6.92×10-7 m3/s). Butler reports similar femoral blood flows for mallard ducks (Anas platyrhynchos) – 30–70 ml/min with an average of ~50 ml/min (Butler, 1982). Johansen and Wesley Millard report similar blood flows for the Giant Fulmar Antarctic bird – on average 40 ml/min (Fig. 4, thermoneutral body core conditions) (Johansen and Wesley Millard, 1973). The small arteries flow rates were assumed proportional to those of the large arteries based on their radii cube ratio in accordance with Murray's law, yielding a flow rate of 4.8×10-9 m3/s and a total flow rate to half the leg (one large and three small arteries) of 7.06×107 m3/s (Murray, 1926; Sherman, 1981; Revellin et al., 2009). Mass conservation (blood flow rate in=blood flow rate out) and again assuming the flow is proportional to radii cube ratio in accordance with Murray's law, yielded the flow rate in the two large veins (2.6×10-7 m3/s each), superficial vein (2.7×10-8 m3/s) and six small veins (2.7×10-8 m3/s each).

lateral leg regions (e.g., air velocity) were neglected. The distances of the main arteries and peripheral veins from the leg exterior were evaluated by image processing (Fig. 1e) and averaged (to maintain symmetry), thus yielding (12.2+7.2)/2=9.71 mm and (1.4+1.7)/ 2=1.54 mm, respectively. The vessels were assumed parallel (no helical structure). The error involved with this assumption was evaluated in detail and shown to be well below 15% (see Supplementary material, Section 1). Implementing all the above mentioned idealizations yielded the solid and finite element models presented in Figs. 1h and i, respectively. An interactive 3D model of the penguin configuration is available in the Supplementary material, Section 2. 2.2. Blood flow rates Flow rates were adopted from Millard et al., (1973). The authors measured the femoral artery flows of two penguin species (wild type birds) – Adelie (Pygoscelis adeliae, three animals) and Gentoo (Pygoscelis papua, four animals). These species are similar in weight to the Humboldt. They used a 3 mm flow transducer placed on the artery through a dorsal incision. Average values were 24 and 59 ml/min for 70

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2.3. Blood flow regime

Table 2 Penguin metabolic rates.

The Reynolds number (Re≡VD/ν, where V is the average blood velocity inside the vessel, D – the vessel diameter and ν is the blood kinematic viscosity) indicates the flow regime. The average blood velocities (flow rate divided by cross sectional area) for the large arteries and veins are 3.04 and 7.95 m/s, respectively. For the kinematic viscosity of penguin blood we used the averaged measured values of four species (Gentoo, Adelie, Chinstrap and Little) (Clarke and Nicol, 1993; Block and Murrish, 1974; Guard and Murrish, 1975). The resulting viscosity range (4.6–13.8 centi-Poise) considers the changes in blood rheology as a function of temperature (5–38 °C), shear rate, hematocrit and plasma protein concentration. This range yielded resulting Reynolds number ranges of 119–353 and 118–350 for the large arteries and veins, respectively (small vessels presented Reynolds numbers well below 100). Penguin blood viscosity is slightly higher than human blood viscosity (Guard and Murrish, 1975; Nichols et al., 2011). Human blood viscosity range for the same conditions (3.9–10.3 centi-Poise) yields the resulting Reynolds number ranges of 159–422 and 157–419 for the large arteries and veins, respectively (again with small vessels presenting Reynolds numbers below 100). Assuming pipe like (Poiseuille) flow, all these values are well within the laminar regime.

Reference

Page

Metabolic rate [W/Kg]

Penguin weight [kg]

Pinshow et al. (1975) Gilbert et al. (2008) Chappell et al. (1989) Stahel and Nicol (1982) Cherel et al. (1993) Cherel (1995) Portugal and Guillemette (2011) Gilbert et al. (2008) McCafferty et al. (2013)

128 131 319 93 267 211 332

2.93 1.65 9.80 4.93 4.23 10.00 4.27

23 38 3.98 4.8 5.915 5.1 16

7 3

3.53 1.50

38 38

(1.98–4.93 W/kg) and within the range for never immersed (NI) juvenile and adult Gentoo penguins exposed to −30 to +30 °C ambient air temperature (~3.2 to ~8.8 W/kg, extreme values representing −30 °C) (Dumonteil et al., 1994). We assumed the penguin tissues thermal material properties are similar to those of humans, Table 3 (Hasgall et al., 2015). Using the tissue density (1102 kg/m3) we evaluated the volumetric metabolic rate – Qv=6.87 W/kg×1102 kg/m3=7570 W/m3.

2.4. Human configuration control 2.6. Humboldt penguin environment As control for the RT phenotype, a human scaled configuration was constructed based on the leg cross section as made just distal to the middle of the tibial diaphysis (section #D7, Figs. 3a-b) (Faure and Merloz, 1987). The leg cross section was assumed of similar dimensions to that of the penguin (25.7 mm diameter). However, the quantity of arteries and veins and their locations in the cross section agrees with the human leg (Fig. 3c). Here, in contrast with the penguin anatomy, seven veins are superficial rather than one. The internal potentially heat exchanging vessels are illustrated in details A, B and C that present the Posterior Tibial vessels (a small artery and a large vein), Anterior Tibial vessels (a large artery and a small vein) and Peroneal vessels (a large artery and two small veins), respectively. As can be seen, this configuration cannot be idealized as symmetric so a full leg was modeled and analyzed (Fig. 3d). Note that the number of large arteries is identical for both configurations (two) but not the number of small arteries, neither that of the veins. The vessel flow rate was again assumed proportional to its radius cube in accordance with Murray's law. Here, yielding a total flow rate to the entire leg of 1.39×10-6 m3/s (1.7% deviation from the penguin configuration). Blood mass conservation facilitated calculating the flow rates in the one large vein (6.8×10-7 m3/s), seven superficial veins (7.1×10-8 m3/s each) and three small veins (7.1×10-8 m3/s each). The resulting average velocity for the large arteries and vein are 3.04 m/s and 20.87 m/s, respectively. Again presenting values well inside the laminar regime. An interactive 3D model of the human configuration is available in the Supplementary material, Section 3.

Foot tissue temperatures and climate conditions were taken from a study on Humboldt penguins living in captivity at Vancouver, Canada (Drent and Stonehouse, 1971). Body temperature was measured using attached thermistors at three positions: deep in the gullet, the skin on the back (beneath the feathers) and the foot (Fig. 4b). Climate conditions (temperature, wind speed and precipitations) were recorded at the birds’ environment (zoo) (Fig. 4c). Fig. 4b indicates the foot temperature is linearly dependent on ambient temperature with the empirical equation Tfoot=1.44·Tair+1.1 °C. Fig. 4c indicates the minimal wind (ambient) temperature is 0 °C (January). In this case, the foot temperature is 1.1 °C. For air at 0 °C we have the following material properties: Kinematic viscosity of ν=1.33×10-5 m2/s, Thermal diffusivity of α=1.85×105 m2/s and Heat conductivity of k=0.024 W/m/K (Webpage). Bergman et al. provide the heat transfer correlation for a cylinder (the modeled leg) in cross flow: NuD=C·ReDm·Pr⅓ where NuD, ReD and Pr are the Nusselt (diameter driven), Reynolds (diameter driven) and Prandtl dimensionless parameters and C and m are correlation constants determined by the flow characteristics, respectively (Bergman et al., 2011). The Reynolds number is: ReD≡V·D/ν, where V=4 m/s is the maximal wind velocity (Fig. 4c, although this value corresponds with March we were conservative and used it), D=25.7 mm the cylinder (leg) diameter and ν is the air kinematic viscosity (provided above). For the calculated Reynolds (7729) the correlation constants are: 4000≤ReD≤40,000→C=0.193, m=0.618 (Bergman et al., 2011). The Prandtl number is: Pr≡ν/α, where ν and α are the kinematic viscosity and thermal diffusivity of air, respectively. For the above air properties we have Pr=0.719. We thus received a Nusselt number of 43.7 for the leg and Tarsometatarsus that enabled calculating the advective heat transfer coefficient: NuD≡h·D/k→h=40.8 W/m2/K. For the foot we employed a similar procedure but using the correlation for a flat plate in parallel flow (Bergman et al., 2011). Here, the Reynolds (ReL – length driven, L=70.2 mm) equals 21,113 and the Prandtl is identical (0.719) – yielding the correlation constants: 0.6≤Pr→C=0.332, m=⅓ (Bergman et al., 2011). We thus received a Nusselt number of NuL=8.2 for the foot and an advective heat transfer coefficient of h=2.81 W/m2/K.

2.5. Metabolic rate and thermal material properties Heat generation (metabolism) must be taken into account when thermal analysis is performed. Table 2 summarizes several representative penguin metabolic rates as documented in the literature. These metabolic rates are not activity related nor species, hence the weight dependence. Non-linear regression indicates the metabolic rate (Q [W/ kg]) follows the empirical relation Q=17.49 Mp-0.58 where Mp is the penguin mass in kg (Fig. 4a). Substituting 5 kg for the mass yields a metabolic rate of 6.87 W/kg and a total metabolic heat production of QTotal=34.35 W. This value is conservative compared with values reported by Dumonteil et al. for penguins in resting conditions 71

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Fig. 4. Penguin data. (a) Curve fitting of the penguin metabolic rate as a function of its mass, generated using Excel. Relevant references are detailed in Table 2. (b) Body temperature measured using thermistors attached at three positions: deep in the gullet (top line), the skin on the back (beneath the feathers, middle line) and the foot (bottom line) (Drent and Stonehouse, 1971). Each point represents the mean of three birds’ measurements, each bird was recorded for ten minutes and the relevant values were averaged. Foot temperature is linearly dependent on ambient temperature. Arrows indicate values extracted using Adobe Photoshop CS 6 and used to calculate the linear regression equation. (c) Climate conditions (temperature, wind speed and precipitations) at the birds’ environment (zoo) (Drent and Stonehouse, 1971). Plotted are long-term monthly means. Arrows indicate the highest wind speed and the lowest air temperature used in our analysis.

Pr=0.725 and NuD=54.8 and ReL= 30,259, NuL=9.3 for the leg/ Tarsometatarsus and foot, respectively. Thus yielding heat transfer coefficients of h=47.9 W/m2/K and h=2.98 W/m2/K for the leg/ Tarsometatarsus and foot, respectively.

Table 3 Thermal material properties used in the analysis. Material

ρ [kg/m3]

Cp [J/kg/K]

k [W/m/K]

Blood Vessel wall and tissue

1050 1102

3617 3306

0.52 0.46

2.8. Blood vessels temperatures Blood vessel temperatures were adopted from a study of the Southern Giant Petrel (Macronectes giganteus, a.k.a. Giant Fulmar) Antarctic bird (Johansen and Wesley Millard, 1973). Johansen and Millard measured intravascular blood temperature along the birds’ feet vessels using catheters containing small thermistors following immersion in cold (−2 to 0 °C) or hot 35–40 °C) seawater. The authors showed that the Southern Giant Petrel body core temperature is on average 39 °C, that feet intraarterial blood temperature can range from 7 °C (cold conditions) to body core (hot conditions) and that feet intravenous blood temperature can range from 1.5 °C (cold conditions) to 37 °C (hot conditions), with cold conditions intravascular temperatures presenting substantial fluctuations following extended immersion (Figs. 8a, 9a and 9b of their study). Schneider et al. studied different kinds of penguins from the equator to the Antarctic Circle (AZA Penguin Taxon Advisory Group, 2014). The authors indicate penguins

2.7. Emperor penguin environment As control for a very harsh environment, the Humboldt penguin model was challenged to maintain thermal homeostasis under the climate conditions of the Emperor penguin breeding colony in Antarctica (McCafferty et al., 2013). McCafferty and coworkers studied the penguin's body temperature distribution in this natural habitat using a thermal camera. Their data provides the foot tissue temperature. The lowest obtained value is −18 °C. They also provide climate conditions: maximal wind velocity of V=5 m/s and minimal wind (ambient) temperature of T=−22 °C, for which the Kinematic viscosity, Thermal diffusivity and Heat conductivity are ν=1.16×10-5 m2/s, α=1.6×10-5 m2/s and k=0.0225 W/m/K, respectively (Webpage). The corresponding dimensionless parameters are: ReD= 11,078, 72

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Section 2.8):

have an average body core temperature of 37.8–38.9 °C (i.e., on average 38.35 °C), similar to that of the Southern Giant Petrel. Nevertheless, the birds are not identical in weight and anatomy and climate conditions also differ. Therefore, we accounted for a wider range than Johansen and Millard (for cold conditions only) and employed three values representing high, moderate and low temperature climate. For the blood going into the arteries at the leg top (Tarteries in), the blood leaving the arteries at the foot (Tarteries out) and for the blood entering the veins at the foot (Tveins in) we thus used [38 °C, 30 °C, 25 °C], [20 °C, 10 °C, 1 °C] and [10 °C, 5 °C, 1 °C], respectively. This range is wider than the Adelie penguin foot temperatures reported by Kooyman et al. (Table 2, 23–36 °C for 13–15 °C air environment and 5 °C for 5 °C water environment), the Gentoo foot temperatures (5–30 °C) reported by Wilson et al. and the Gentoo foot temperatures reported by Dumonteil et al. (Fig. 3, 1–10 °C for −30 °C air environment) (Kooyman et al., 1976; Wilson et al., 1998; Dumonteil et al., 1994). It also exceeds the femoral vein temperature range (37.5–38.7 °C) and the foot dorsal vein temperature range (3.7–37.6 °C) of emperor penguins diving under sea ice (Table 1) (Ponganis et al., 2003). We therefore received 27 combinations for which we had to evaluate the heat exchanger efficiency that reduced to 21 following imposing the physiological constraints Tveins in≤Tarteries out≤Tarteries in.

T = Tveins in = 10°C /5°C /1°C

(4)

External: All external (air) boundaries represented advective and radiative heat transfer depending on the environment case assumed (see Sections 2.6–2.7). The radiation boundary condition takes the form: 4 −∼n⋅(−k ∇T ) = εσ (T Amb − T 4)

(5)

where ∼n is the normal to the domain boundary surface, σ=5.67×108 W/m2/K4 the Stefan – Boltzmann constant, TAmb - the environment (air) temperature and ε~1 is the emissivity of birds feathers and skin (close to that of a perfect black body) (Jordan and Dale, 1963). The advection boundary condition takes the form:

−∼n⋅(−k ∇T ) = h(TAmb − T )

(6)

Here, h - the heat transfer coefficient - is both environment case dependent and changes between the leg and the foot according to the appropriate correlation (see Sections 2.6–2.7). Heat transfer by conductivity at the air boundaries was neglected. The foot sole (bottom side of the trapezoidal prism) was conservatively assumed fully equilibrated with Tground - the ground temperature - (no contact resistance) to impose the highest heat loss on the model:

2.9. Penguin vs. human comparison

T = TGround

The climate boundary conditions and vessel temperature combinations listed above were implemented and analyzed for both human and penguin models and an average value for the blood leaving the veins at the leg top (Tveins out) has been calculated. To evaluate the efficiency difference between the two configurations the total heat exchanged to the veins (recovered) in each configuration was evaluated: QExchanged =ρblood·Cp blood·V̇ ·(Tveins out - Tveins in) where ρblood, Cp blood and V̇ are the blood density, blood heat capacity and the corresponding vein blood flow rate. We define the efficiency discrepancy factor (Ef) as the difference between the total heat exchanged to the veins in each configuration (multiplied here by two for both legs) normalized to the total metabolic heat production: Ef ≡2·(QExchangedpenguin–QExchangedhuman)/QTotal.

(7)

where the ground temperature depends on the environment case assumed (see Sections 2.6–2.7). For the blood leaving the veins at the leg top we assumed the temperature is nearing its axial asymptotic value. This condition was enforced using zero axial (normal) heat flow at the veins outlet. This condition is common at the outlet of efficient heat exchangers (Bergman et al., 2011):

−∼n⋅(−k ∇T ) = 0

(8)

At the trunk interface, we assumed a prescribed heat flow rate (Qtrunk). Its value was taken nearly zero (0.01 W) at start and was increased iteratively until energy conservation was achieved (see Section 2.11):

2.10. Finite element analysis

i −∼n⋅(−k ∇T ) = Qtrunk /A

The finite element analysis (FEA) was performed using the commercial package COMSOL. The underlying physics was heat transfer including conduction (heat diffusion) and advection (fluid convection mediated heat flow). The solved equation is:

The trunk heat flow (Qtrunk) was applied as a normal distribution (Gaussian) centered at the leg axis with a standard deviation equal to 20% of the leg diameter. This procedure reduced the number of iterations required for convergence from 5 to 7 per configuration (when using a constant heat flow distribution) to 2–3 due to reduced artificial heat loss at the leg surface. Material properties were taken as human (see Section 2.5). The analysis followed the COMSOL guidelines for analyzing heat exchangers. A simplified model analyzing a single artery and vein couple was validated against a recent study scrutinizing the doubletube counter-flow heat exchanger and results agreed very well (temperature discrepancies were below 1%, data not shown) (Laskowski, 2015). Tissue was analyzed using heat transfer in solids physics (∼v = 0 ). Blood domains (lumens) were analyzed using heat transfer in fluids physics. Here, blood velocity distribution was modeled as laminar pipe (Poiseuille) flow with an average fluid velocity taken from the flow rates of Section 2.2. Blood thermal conductivity was not neglected. For the penguin configuration, the PARADISO direct nonlinear solver was chosen. The solver converged using a damped Newton iteration method (damping factor of 1e-2 to 1e-6). A nested dissection multithreaded row preordering algorithm, a pivoting perturbation of 1e-8 and streamline and crosswind diffusion stabilization were used. The shape functions for the temperature were quadratic. The mesh generated was mixed, consisting of both swept prism elements (leg and foot regions) and free meshed tetrahedral elements (Tarsometatarsus region), Figs. 1i and

ρCp∼v⋅(∇T ) = ∇⋅(k ∇T ) + q

(1) 3

where ρ is the material density [kg/m ], Cp - the material heat capacity [J/kg/K], ∼v - the blood velocity [m3/s] (relevant only for fluid domains – lumens), T - temperature field [K], k - thermal conductivity [W/m/K], q - heat generated by metabolic activity as volumetric heat generation [W/m3] (see Section 2.5),⋅ - scalar product operator and ∇ is the gradient operator. The boundary conditions were: Internal: Blood and tissue were assumed fully equilibrated at the vessels boundaries (full temperature and heat flux continuity). For the blood going into the arteries at the leg top we assumed (see Section 2.8):

T = Tarteries in = 38°C /30°C /25°C

(2)

For the blood leaving the arteries near the foot we assumed (see Section 2.8):

T = Tarteries out = 20°C /10°C /1°C

(3)

For the blood entering the veins near the foot we assumed (see 73

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iteration served as the boundary condition for the next iteration. Convergence was achieved when the calculated heat flowing from the trunk stabilized to a change below 0.01 W. At steady state, the total heat leaving the leg (QOut, by advection - QAdvection and by radiation QRadiation, calculated by the finite element software) was equal to the heat entering it from the trunk plus the metabolic heat generated within the leg: QTrunk+QMetabolic=QOut=QRadiation+QAdvection. The metabolic heat generated for half the leg is: QMetabolic=Qv·[½ Leg volume] =7570 W/m3·0.000043 m3=0.327 W, where we used the Computer Assisted Design (CAD) software to evaluate the model volume (simple summation of two cylinders and a trapezoid prism yields a 2.8% volume error).

3d. The number of elements and degrees of freedom was ~ 60,000 and ~ 140,000, respectively. For the human configuration these values more than tripled so an iterative solver was applied (GMRES, incomplete LU, default COMSOL settings).

2.11. Body core (leg top) thermal equilibration Thermal equilibration with the body core must be accounted for. We employed integral energy conservation with the leg as the control volume and evaluated the heat flow from the trunk to the leg. The calculation is iterative. First, a nearly zero heat flow was assumed (0.01 W). Then, the energy deficit derived from each finite element

Fig. 5. Results. (a) Leg temperature distribution [°C] for the penguin configuration, Humboldt captivity environment (Tarteries in=38 °C, Tarteries out=Tveins in=1 °C), generated using COMSOL. (b) Same as (a) for the human configuration. (c) Same as (a) for Emperor penguin environment. (d) Efficiency discrepancy factor (Ef) as a function of the arteries (Tarteries in) and veins (Tveins in) inlets and the arteries outlets (Tarteries out) blood temperatures in 2D form, generated using Excel. (e) Same as (d) in 3D form, generated using MATLAB. (f) Same as (a), presented within equally distanced transverse planes.

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The energy deficit of each finite element iteration i is Δ (i)≡QOut(i)–QTrunk(i)–QMetabolic since more heat is initially leaving the leg than entering it [ QTrunk(i=1)~0]. The previous deficit served as the boundary condition for the next iteration: QTrunk(i+1)=QTrunk(i)+Δ(i). This procedure persisted until the total energetic error (ε) dropped to below 0.01 W (convergence criterion): ε≡|QTrunk(i +1)–QTrunk(i)|≤0.01 W. Representative calculations are available in the Supplementary material, Section 4.

uration; thus making the Rete probably crucial for penguin thermal endurance. The calculations presented in the study (Figs. 5d–e) may partially overestimate the RT energetic benefits. They could represent a too high temperature for the blood flowing into the leg arteries (Tarteries in) or a too low temperature for the blood leaving the foot veins (Tveins in). Furthermore, a more detailed model accounting for different tissue layers (e.g., skin, fat and muscle) could show more accurate results. Unfortunately, literature lacks data on the anatomical characteristics of such layers and their corresponding thermal properties in penguins. Nonetheless, even considering the presented model and the lowest value of the efficiency discrepancy between the penguin and human configurations (~25%), this study clearly indicates the significance of the RT as a heat exchanger. Particularly considering the fact that all Ef values are underestimated since we modeled a fully parallel heat exchanger and neglected the partially helical structure of the Rete that can improve its efficiency by up to ~15% (see Supplementary material, Section 1). The evolutionary stress involved with energetic demands that are increased by more than 25% is considerable. Moreover, results indicate that most heat transfer takes place at the proximal part of the Rete (Fig. 5f). This further substantiates the fact that the RT thermally isolates the foot from the body core quite well. In addition, our study does not incorporate the fact that human basic metabolic rate (BMR, typically < 2 [W/Kg]) is lower than the Humboldt penguin's (Henry, 2007). We also do not fully address the actual blood velocities in human vessels and the probably different tissue thermal properties between the two species (density, heat capacity and heat conductance) such as the penguin foot that is probably uniquely adapted to withstand extreme climate. In fact, we intentionally eliminate these factors by using the same metabolism, material properties and blood velocities in all configurations in order to focus on the RT physiological and anatomical advantages. Nonetheless, these inaccuracies as well do not diminish the remarkable order of magnitude of the Rete contribution to the penguin thermal endurance. Interestingly, penguins (~5 kg animals in this study) have more blood vessels in their legs than humans do (50–60 kg minimum). It appears reasonable that the origin of the abundant vessels is not mass transfer limitation but rather heat transfer advantages. Bergman et al. define the overall heat transfer coefficient (U) for a heat exchanger (chapter 11, Page 708) (Bergman et al., 2011): (UA)−1≡RTotal=(hA)c1 +RWall+(hA)h-1 where c and h subscripts, h, A=πdL, RTotal and RWall denote cold (here vein) and hot (here artery) vessels, convection (here blood) heat transfer coefficient, vessel surface area, total and wall conduction (here tissue) heat transfer resistances, respectively. Our employed human scaling is conservative insofar as since the vessels should grow, the ratio between the perimeter (surface area) and the cross sectional area (volume) should decrease and the heat transfer efficiency is expected to reduce. Therefore, the efficiency of the human configuration in terms of heat transfer will probably be even lower than that assumed in this study. The factor 4/d can be used to roughly evaluate the scaling effect: Blood vessel surface area per length (P)/ Blood vessel volume per length (A)≡πd/(πd2/4)==4/d→d↑→P/A↓. This scaling characteristic could be a limiting factor indicating why solutions similar to that of the penguin are less effective for large animals or at the large vessel level. It follows that any efficient utilization of biological heat exchanging technique should involve employment of numerous small diameter vessels and could account for the increased blood vessel number present in the penguin. The scaling law also motivates particular study of large penguin species (e.g., Emperor) to examine possible unique RT adaptation in animals of considerably larger mass. This study may misrepresent the Humboldt penguin environment as mild vs. that of the Emperor. In order to properly examine environmental thermal stress, the animal thermal neutral zone (TNZ) needs to be addressed. The TNZ is an ambient temperature range for which the animal metabolic rate does not have to increase in order to maintain its

3. Results Results show that the penguin configuration retains significantly more heat than the human configuration, thus demonstrating the advantages of the RT phenotype in terms of thermal endurance. Most heat transfer takes place at the proximal part of the leg, thus demonstrating the efficient function of the RT in thermally isolating the foot from the body core. As expected, the Humboldt penguin model cannot withstand the harsh climate conditions of the Emperor penguin. 3.1. Humboldt penguin environment Figs. 5a–b present the leg temperature distribution for the penguin and human configurations, respectively (Tarteries in=38 °C, Tarteries out=Tveins in=1 °C). Both configurations can maintain reasonable (and similar) thermal homeostasis though the penguin configuration retains ~20.35 W from the RT while the human configuration only 9.05 W. This environmental combination represents an extreme case. When conditions are milder the gap between the two configurations in terms of heat retained reduces (e.g., to ~8.5 W vs. ~4 W in Tarteries in=25 °C, Tarteries out=20 °C, Tveins in=10 °C environment). 3.2. Emperor penguin environment Fig. 5c presents the leg temperature distribution in the emperor environment. The Humboldt penguin cannot maintain reasonable thermal homeostasis if in order to do so the body core temperature must exceed 80 °C. Furthermore, in order to achieve thermal steady state the penguin needs to provide ~100 W from the torso interface. For a penguin generating 34.35 W of metabolic heat this dissipation rate appears intolerable since it does not even account for other window (heat losing) regions such as the face and flippers. The Humboldt penguin model cannot withstand the harsh climate conditions of the Emperor penguin (as expected). 3.3. Penguin vs. human comparison Figs. 5d–e demonstrate that, as expected from a counter-current heat exchanger, the larger the inlets temperature difference (Tarteries in–Tveins in) the more heat is transferred from arteries to veins and the higher the efficiency discrepancy factor (Ef). Thus, the lower the ambient temperature (colder climate) the more efficient is the penguin configuration vs. its human counterpart. The penguin RT can contribute to 25–65% metabolic heat conservation. Fig. 5d also indicates that the arteries temperature as they leave the heat exchanger (Tarteries out) and enter the foot is of negligible significance. This is expected as results indicate that most heat transfer takes place at the Rete proximal region (where hot blood enters the exchanger), Fig. 5f. All calculated efficiency discrepancy factors are tabulated in the Supplementary material, Section 5. 4. Discussion We quantitatively link here for the first time the function versus the structure of the extraordinary Rete physiological phenotype. Our study indicates that the RT retains 25 − 65% of the Humboldt species total metabolic energy production as compared with a human-like config75

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similar in size to our small arteries (below the terminal arterial branch) are expected to be well equilibrated with the tissue temperature while those larger in diameter than 300 µm (like the leg two main arteries) are not expected to equilibrate with local tissue but to maintain a temperature slightly below the body core (heart) due to their increased thickness and thus thermal insulation. The vein branches of the circulation tree present a different case. Here, significant divergence from tissue temperature is delayed to vessels on the order of 750 µm rather than 300 µm. This is well expected as veins are thinner and less thermally insulated than arteries. According to this figure, all the study models vessels should be well equilibrated with the tissue temperature but the leg two main arteries. Nevertheless, Datta addresses the human case where the environment is relatively mild, the body is originally well-insulated by clothes and the distance between cold and warm vessels is in most cases larger. In contrast, as we observed in this study, for the penguin leg case – where conditions are much harsher, no clothing is available and the leg dimensions are much smaller (closer arteries and veins) – thermal equilibration with the tissue is limited to the distal Rete/leg regions. Furthermore, it is highly probable that for penguin species occupying harsher climate conditions, blood throughout the foot is also not fully thermally equilibrated with the tissue. Blood cannot flow below zero degrees due to freezing while tissue temperature is certainly at least partially equilibrated with the environment (−18 °C for the Emperor penguin for example) (McCafferty et al., 2013). Thus providing further support to the dichotomy of the human and penguin blood - tissue thermal equilibration characteristics. The penguin foot tissue (sole) is probably uniquely adapted to its extreme environment and a comprehensive study of this tissue is well advocated since this assumption is not yet physiologically substantiated. Fig. 6b presents the penguin blood temperature equilibration. Here, there are substantial temperature differences over a very short distance yielding extreme thermal gradients and thus heat flows. In the human body we expect a temperature drop of ~3 °C over a distance of ~0.5 m from the body core to the upper leg for instance (~6 °C/m). In contrast, the penguin Rete tissue can experience a temperature drop of more than 10 °C over a representative distance of ~ 0.5 mm from the artery to the vein (~20,000 °C/m), Fig. 6b. This means a temperature gradient and thus heat flows that are at least three orders of magnitude higher. It is conceivable that such heat flows would bring about tissue burn damage in humans. It is therefore quite sensible to assume that not only the foot tissue but also the Rete regions (and vessels) have undergone evolutionary adaptation. Literature provides numerous references to heat adaptation in animals as well as in humans (Taylor, 2011). A recent study demonstrates penguin adaptations even comprise gene regulation (Dégletagne, 2011). However, while many

resting thermal homeostasis (Woehler, 2014). The emperor penguin TNZ is −10–20 °C (Woehler, 2014). Its environment average air temperature is −22 °C (McCafferty et al., 2013). Therefore, this species is chiefly subjected to cold stress. In contrast, the Humboldt penguin TNZ is 2–30 °C (Simeone et al., 2004). However, in this species case thermal stress also refers to hot climate (26.4–31.4 in Summer at one documented location) (Simeone et al., 2004). Undoubtedly, evolution supports anatomical adaptations that broaden the species TNZ. For example, the physique of the emperor penguin establishes it as the species with the highest tolerance to cold. It is the largest penguin and has the lowest surface area to body mass ratio – most favorable for reducing heat loss to the environment (Woehler, 2014). It is therefore only reasonable to inquire what unique adaptations and thermoregulatory behaviors (TRB) penguins adopted to address hot stress (Fretwell et al., 2014). The Emperor penguin experiences an average air temperature that is 12 °C below its TNZ. This means that without TRB its energy consumption would be intolerable. Here, the TRB expresses as clustering into dense groups (huddles). The dense group formation maintains heat so efficiently that at times the surface temperatures of birds within the huddle can reach ~35 °C (Woehler, 2014). This temperature is too hot for Emperor penguins so they move to the periphery or even to the outside of the huddle to cool. In such a cold environment as the Antarctic the case of hot temperature is only a small problem (perhaps for a short period in late summer). For the Humboldt penguin Simeone et al. (2004) (Fig. 1) show that a predominant TRB is covering the feet during winter while exposing them during summer. Therefore, the penguin probably uses the Rete to its advantage in hot climate as well. Our investigation is currently being expanded to address the effects of feet related TRB (exposed vs. covered) using the advection heat transfer correlations approach detailed above in methods. In addition, to fully address the penguin environmental thermal stress, we are completing our analysis for the full range of blood vessel temperatures detailed above by relinquishing the previously used physiological constraints Tveins in≤Tarteries out≤Tarteries in that represent cold climate. Datta (Fig. 3.10, Page 37) presents a schematic diagram of the temperature equilibration between blood and tissue (Datta, 2002). The illustration is conceptually reconstructed in Fig. 6a. When tissue temperature is lower than blood (lower diagram branch), blood is cooled by the tissue as it travels away from the heart and reaches a minimum temperature at the medium sized vein level where thermal equilibration is reached (not at the microcirculation level, as one would intuitively assume) (Datta, 2002). Then, the blood warms back up as it returns to the heart along the vein branches of the circulation tree by mixing with complementary blood arriving from the body core. Arteries

Fig. 6. Temperature equilibration between blood and tissue in penguin vs. human. (a) The human case. Illustration is conceptually reconstructed from Datta (Fig. 3.10, Page 37) (Datta, 2002). (b) The penguin case.

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Antarct. J. U.S. 9, 98–99. Borley, N.R., Collins, P., Alan, R., Gatzoulis, M.a., Healy, J.C., Johnson, D., 2008. Gray’s Anatomy, 40th ed. Butler, P.J., 1982. Respiratory and cardiovascular control during diving in birds and mammals. J. Exp. Biol. 100, 195–221. Chappell, M.A., Morgan, K.R., Souza, S.L., Bucher, T.L., 1989. Convection and thermoregulation in two Antarctic seabirds. J. Comp. Physiol. B 159, 313–322. Cherel, Y., 1995. Nutrient reserve storage, energetics, and food consumption during the prebreeding and premoulting foraging periods of king penguins. Polar Biol. 15. Cherel, Y., Fréby, F., Gilles, J., Robin, J.P., 1993. Comparative fuel metabolism in Gentoo and King Penguins: adaptation to brief versus prolonged fasting. Polar Biol. 13, 263–269. Clarke, J., Nicol, S., 1993. Blood viscosity of the little penguin, eudyptula minor, and the Adélie Penguin, Pygoscelis adeliae: effects of temperature and shear rate. Physiol. Zool. 66, 720–731. Datta, A.K., 2002. Biological and Bioenvironmental Heat and Mass Transfer. CRC Press, U.S.A. Davis, L.S., Penguin World. Dégletagne, C., 2011. Penguin Acclimatization to Polar Environmental Constraints: A Transcriptomic and Integrative Study in King (Aptenodytes Patagonicus) and Adélie Penguins (Pygoscelis adeliae). https://www.researchgate.net/publication/ 278641357_Penguin_acclimatization_to_polar_environmental_constraints_a_ transcriptomic_and_integrative_study_in_King_Aptenodytes_patagonicus_and_Adelie_ penguins_Pygoscelis_adeliae Université Claude Bernard - Lyon I. Desboefs, F., 1966. Contribution a letude de la vascularisation de membre inferiur des oiseaux en rapport avec la thermoregulation. D.E.S Paris. Drent, R.H., Stonehouse, B., 1971. Thermoregulatory responses of the peruvian penguin, Spheniscus humboldti. Comp. Biochem. Physiol. A Comp. Physiol. 40, 689–710. Dumonteil, E., Barre, H., Rouanet, J.L., Diarra, M., Bouvier, J., 1994. Dual core and shell temperature regulation during sea acclimatization in Gentoo penguins (Pygoscelis papua). Am. J. Physiol. - Regul. Integr. Comp. Physiol. 266, R1319–R1326. Faure, C., Merloz, P., 1987. Transfixation - atlas of anatomical sections for the external fixation of limbs. Saudi Med. J. 33. Filhol, M.H., 1882. Observations relatives a la circulation arterielle dans le membre (Aptenodytes pennati, Eudyptes antpodes et chrysochoma). Bull. Soc. Philos. 7, 243–248. Fretwell, P.T., Trathan, P.N., Wienecke, B., Kooyman, G.L., 2014. Emperor Penguins Breeding on Iceshelves. PLoS One 9, e85285. Frost, P.G.H., Siegfried, W.R., Greenwood, P.J., 1975. Arterio-venous heat exchange systems in the Jackass penguin Spheniscus demersus. J. Zool. 175, 231–241. Gilbert, C., Blanc, S., Le Maho, Y., Ancel, A., 2008. Energy saving processes in huddling emperor penguins: from experiments to theory. J. Exp. Biol. 211, 1–8. Guard, C.L., Murrish, D.E., 1975. Effects of temperature on the viscous behavior of blood from Antarctic birds and mammals. Comp. Biochem. Physiol. 52A, 287–290. Hasgall, P.A., Di Gennaro, F., Baumgartner, C., Neufeld, E., Gosselin, M.C., Payne, D., Klingenböck, A., Kuster, N., 2015. IT’IS Database for thermal and electromagnetic parameters of biological tissues, Version 3.0, September 01st. 〈http://dx.doi.org/10. 13099/VIP21000-03-0〉. 〈www.itis.ethz.ch/database〉. Henry, C.J.K., 2007. Basal metabolic rate studies in humans: measurement and development of new equations. Public Health Nutr. 8, 1133–1152. James, H.F., Olson, S.L., 1949. Flightless birds of New Zealand. Nature 164, 1077–1078. Johansen, K., Wesley Millard, R., 1973. Vascular responses to temperature in the foot of the giant fulmar, Macronectes giganteus. J. Comp. Physiol. 85, 47–64. Jordan, K.A., Dale, A.C., 1963. Calorimetric measurement of heat transmission components of chickens. Trans. ASAE 6, 11–15. Kooyman, G.L., Gentry, R.L., Bergman, W.P., Hammel, H.T., 1976. Heat loss in penguins during immersion and compression. Comp. Biochem. Physiol. Part A: Physiol. 54, 75–80. Laskowski, R., 2015. The black box model of a double-tube counter-flow heat exchanger. Heat Mass Transf. 51, 1111–1119. Livezey, C., 1989. Morphometric patterns in Recent and fossil penguins (Ayes, Sphenisciformes). J. Zool. Lond. 219, 269–307. McCafferty, D.J., Gilbert, C., Thierry, A.-M., Currie, J., Le Maho, Y., Ancel, A., 2013. Emperor penguin body surfaces cool below air temperature. Biol. Lett. 9, 20121192. Midtgård, U., 1981. The rete tibiotarsale and arteriovenous association in the hind limb of birds: a comparative morphological study on countercurrent heat exchange systems. Acta Zool. 62, 67–87. Midtgård, U., 1984. Blood vessels and the occurrence of arteriovenous anastomoses in cephalic heat loss areas of mallards, Anas platyrhynchos (Aves). Zoomorphology 104, 323–335. Millard, R.W., Johansen, K., Milsom, W.K., 1973. Radiotelemetry of cardiovascular responses to exercise and diving in penguins. Comp. Biochem. Physiol. Part A: Physiol. 46, 227–240. Murray, C.D., 1926. The physiological principle of minimum work: I. The vascular system and the cost of blood volume. Proc. Natl. Acad. Sci. USA 12, 207–214. Netter, F.H., 2014. Atlas of Human Anatomy. Nichols, W., Rourke, M., Vlachopoulos, C., 2011. McDonald's Blood Flow in Arteries. Theoretical, Experimental and Clinical Principles. CRC Press, Taylor & Francis Group, U.S.A.. http://www.crcnetbase.com/isbn/9781444128789. Ninomiya, H., Yamazaki, K., Inomata, T., 2013. Comparative anatomy of the vasculature of the dog (Canis familiaris) and domestic cat (Felis catus) paw Pad. Open J. Vet. Med. 03, 11–15. Pinshow, B., Battles, D.R., Pinshow, H., Schmidt-Nielsen, K., 1975. Emperor penguins: thermoregulation and locomotion. Antarct. J. 10, 127–129. 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address adaptation to temperature changes and to temperature changes kinetics, to the best of our knowledge we are not familiar with documented tissue adaptation to heat flows. It does not appear reasonable that such adaptation will phenotypically present itself dominantly at the intravascular compartment but rather at the tissue protein, extracellular space and electrolyte regions. This hypothesis remains an open question at present since such a study is not within the scope of this contribution. 5. Conclusions This study examines the RT significance for the thermal endurance of medium sized (~5 kg) non-Antarctic penguin species. We base our model on the Humboldt penguin. We show that the Rete existence results in blood occupying the foot expressing a lower average temperature and thus the penguin loosing significantly less heat to the ground. Most heat transfer takes place at the proximal part of the leg, thus demonstrating the highly efficient function of the RT in thermally isolating the foot from the body core. The RT retains 25 − 65% of the Humboldt species total metabolic energy production as compared with a human-like configuration; thus making the Rete probably crucial for penguin thermal endurance. Here, we quantitatively link for the first time the function versus the structure of this remarkable physiological phenotype. Conflict of interest The authors declare that no conflict of interest exists with relation to the contents of this manuscript. Author contributions Saar Golan conceived the research, Shaked Kazas and Moran Benelly gathered the anatomical and physiological data and performed the calculations, All analyzed the data and interpreted the results. Shaked Kazas and Moran Benelly drafted the manuscript. Saar Golan edited and revised the manuscript. All approved the manuscript final version. Saar Golan addressed the reviewers’ comments and drafted the revision. Acknowledgments We are deeply grateful to Dr. Roi Lapid, the Veterinarian of the Hai Park Zoo (79th Ha-Hashmonaim Street, Qiryat Motzkin, 2633761, Israel) for the Humboldt penguins dimensional data. We are deeply grateful to Rotem Guzman the devoted and knowledgeable penguin caretaker and to Dr. Gillad Goldstein the curator of the Tel Aviv - Ramat Gan Zoological Center for the penguin images, visits and explanations. We are deeply grateful to David Salomon for his remarkable Humboldt images and numerous penguin related explanations. Appendix A. Supporting information Supplementary data associated with this article can be found in the online version at http://dx.doi.org/10.1016/j.jtherbio.2017.04.011. References Atalgin, H., 2011. Morphological observation of the Rostral Epidural Rete Mirabile (Rete Mirabile Epidurale Rostrale) in the Saanen Goat. Atatürk Üniv. Vet. Bil. Derg. 6 (3), 177–181. AZA Penguin Taxon Advisory Group, 2014. Penguin (Spheniscidae) Care Manual, Silver Spring. Bergman, T.L., Lavine, A.S., Incropera, F.P., DeWitt, D.P., 2011. Fundamentals of Heat and Mass Transfer, 7th ed. John Wiley & Sons, Inc, U.S.A. Block, G.A., Murrish, D.E., 1974. Viscous properties of bird blood at low temperatures.

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Moran Benelly received her B.Sc. in Chemical Engineering in 2010 and her ME in Biomedical Engineering in 2016 for her research in the field of Biomedical flows and heat transfer, from the Technion, Israel Institute of Technology. Moran worked from 2010 to 2013 in Chiasma, in drugs development, where she was responsible for R & D and equipment validation. Since 2013, Moran works for Omrix (Johnson & Johnson Bio-Surgery). Omrix develops biological solutions for severe bleeding. Moran is part of the project management team, leading technology transfer projects for drug products external manufacturing.

penguins diving under sea ice. Comp. Biochem. Physiol. Part A: Mol. Integr. Physiol. 135, 477–487. Portugal, S.J., Guillemette, M., 2011. The use of body mass loss to estimate metabolic rate in birds. Comp. Biochem. Physiol. Part A Mol. Integr. Physiol. 158, 329–336. Revellin, R., Rousset, F., Baud, D., Bonjour, J., 2009. Extension of Murray's law using a non-Newtonian model of blood flow. Theor. Biol. Med. Model. 6, 7. Rohen, J.W., Yokochi, C., Lütjen-Drecoll, E., 2015. Anatomy, A Photographic Atlas. LWW, North American Edition (February 4, 2015). Sherman, T.F., 1981. On connecting large vessels to small. The meaning of Murray's law. J. General Physiol. 78, 431–453. Simeone, A., Luna-Jorquera, G., Wilson, R.P., 2004. Seasonal variations in the behavioural thermoregulation of roosting Humboldt penguins (Spheniscus humboldti) in north-central Chile. J. Ornithol. 145, 35–40. Stahel, C.D., Nicol, S.C., 1982. Temperature regulation in the little penguin,Eudyptula minor, in air and water. J. Comp. Physiol. B 148, 93–100. Taylor, N.A.S., 2014. Human heat adaptation. Compr Physiol. 4 (1), 325–365. http://dx. doi.org/10.1002/cphy.c130022.. https://www.ncbi.nlm.nih.gov/pubmed/ 24692142. Trawa, G., 1970. Note preliminaire sur la vascularisation des membres des Spheniscides de terre Adelie. L'Oiseau e 142–156. Webpage, Fluid Properties Calculator. Microelectronics Heat Transfer Laboratory, Department of Mechanical Engineering, University of Waterloo, 〈http://www.mhtl. uwaterloo.ca/old/onlinetools/airprop/airprop.html〉. Website,Museum of Osteology. Wikipedia, Humboldt Penguin, Photographer: Christian Mehlführer. Wilson, R.P., Adelung, D., Latorre, L., 1998. Radiative heat loss in gentoo penguin (Pygoscelis papua) adults and chicks and the importance of warm feet. Physiol. Zool. 71, 524–533. Woehler, E.J., 2014. Penguins: The Animal Answer Guide 26. Kooyman G.L. and Lynch W. John Hopkins University Press, Baltimore, pp. 599.

Dr. Saar Golan received his engineering degrees from the Technion. He is faculty at Ariel University (Chemical and Mechanical Engineering departments) and an adjunct lecturer at the Technion (Biomedical Engineering) since 2014. Dr. Golan is the head of the Bio-analytical Microsystems Lab in Ariel. His research interests involve biomechanics, cancer and early embryonic development (implantation). He is keenly involved with clinical studies, medical implants development and biological heat/mass transfer and thermoregulation. Dr. Golan maintains close scientific collaboration with several leading Israeli medical centers.

Shaked Kazas received his B.Sc. in Mechanical Engineering in 2010 and his ME in Biomedical Engineering in 2016 for his research in the field of Biomedical flows and heat transfer, from the Technion, Israel Institute of Technology. He worked as a Multidisciplinary Designer (2010–2013), Team Leader (2014–2015) and currently as a Project Manager in several divisions of the Ministry of Defense, Israel.

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