applied sciences

Article Reverse Engineering of Thermoregulatory Cold-Induced Vasoconstriction/ during Localized Cooling

Ali Youssef 1 , Anne Verachtert 1, Guido De Bruyne 2 and Jean-Marie Aerts 1,*

1 Department of Biosystems, Animal and Human Health Engineering Division, M3-BIORES: Measure, Model & Manage of Bioresponses Laboratory, KU Leuven, Kasteelpark Arenberg 30, 3001 Heverlee, Belgium 2 Department of Product Development, University of Antwerp, 2000 Antwerp, Belgium * Correspondence: [email protected]

 Received: 10 July 2019; Accepted: 8 August 2019; Published: 16 August 2019 

Abstract: Biological systems, in general, represent a special type of control system. The physiological processes of , which serve to maintain the organism’s internal equilibrium against external influences, are clear forms of biological control system. An example of the homeostasis is the control of the organism thermal state or the thermoregulation. The thermoregulatory control of human blood flow, via vasoconstriction and vasodilation, is vital to maintaining normal body temperatures during challenges to thermal homeostasis such as localised cooling. The main objective of this paper is to reverse engineer the localised thermoregulatory cold-induced vasoconstriction/vasodilation (CIVC/CIVD) reactions using a data-based mechanistic approach. Two types of localised cooling were applied to the fingers of 33 healthy participants, namely, continuous and intermittent cooling. Modelling of the thermoregulatory cold-induced vasoconstriction/vasodilation reactions suggested two underlying processes, with one process being 10 times faster. A new term is suggested in this paper, namely, the latent heat of CIVD, which represents the amount of dissipated heat required to trigger the CIVD. Moreover, a new model for the thermoregulatory localised CIVC/CIVD reactions is proposed. The suggested new model states that, with an initial vasodilation state, the initial localised CIVC is triggered based on a certain threshold in the rate of heat dissipation from the skin to the surrounding environment.

Keywords: thermoregulation; homeostasis; cold-induced-vasodilation; cold-induced-vasoconstriction; control system; dynamic modelling

1. Introduction Biological systems represent a special type of control system. In all of these, control is exercised over the flows of matter and energy to maintain a range of stationarity of their existence [1]. Hence, all living organisms are equipped with numerous interconnected control systems, which serve to maintain the organism’s internal equilibrium regardless of outside influences. This condition is known as homeostasis. In the 19th century, Claude Bernard discovered the “amazing constancy” of the internal environment of the organism [2], and in 1927, Cannon named it the homeostasis [3]. An example of homeostasis is the control of an organism’s thermal state (thermoregulation system). Heat in biological systems is generated in the course of metabolic conversion and scattered by conduction, convection, radiation and evaporation [4–6]. The hands and feet form powerful thermoregulatory regulators in the body, serving as heat radiators (exchanger) and evaporators in hot environments and as thermal insulators in the cold [7]. Taylor et al. [8] estimated that each hand and foot can dissipate 150–220 W m 2 through radiation and · −

Appl. Sci. 2019, 9, 3372; doi:10.3390/app9163372 www.mdpi.com/journal/applsci Appl. Sci. 2019, 9, 3372 2 of 19

Appl. Sci. 2019, 9, x FOR PEER REVIEW 2 of 19 convection at rest in an ambient temperature of 27 ◦C, with even greater heat dissipation through sweating.sweating. Additionally,Additionally, the the extremities extremities can servecan asserv thermale as thermal sensor acting sensor in feedbackacting in and feedback feedforward and fashionfeedforward to the fashion thermoregulation to the thermoregulation system of the system body [7 of]. the body [7]. ArteriovenousArteriovenous anastomosesanastomoses (AVAs) (AVAs) are are direct direct connections connections between between small small arteries and small and veinssmall (Figureveins (Figure1), with 1), no with capillary no capillary section betweensection between them. Since them. there Since is nothere capillary is no capillary transportation, transportation, the only transportthe only transport function they function could they possibly could have possibly is the have transport is the of transport heat from of the heat body from core the to surfacebody core areas to containingsurface areas AVAs containing [9]. AVAs [9].

Figure 1. Schematic diagram showing the effect of a closed (A) and an open (B) arteriovenousFigure 1. Schematic anastomoses diagram on theshowing blood flowthe effect during of cold-induced a closed (A vasoconstriction) and an open ( andB) arteriovenous cold-induced vasodilation,anastomoses respectively.on the blood flow during cold-induced vasoconstriction and cold-induced vasodilation, respectively. Grant and Blond [10] investigated the role of AVA in thermoregulation. They found a relation betweenGrant the and number Blond of [10] AVAs investigated in a body the part role and of theAV changeA in thermoregulation. in local They found due a torelation local coldbetween [11]. the When number the of extremities AVAs in ofa body the handpart and and th feete change are exposed in local locally skin temperature to a cold environment, due to local theircold [11]. AVAs When respond the withextremities sympathetically of the hand mediated and feet vasoconstriction,are exposed locally which to a iscold termed environment, cold-induced their vasoconstrictionAVAs respond (CIVC).with sympathetically CIVC reduces themediated blood flow vasoconstriction, to the peripheries which in favour is termed of a central cold-induced pooling ofvasoconstriction blood in the torso (CIVC). and CIVC deep bodyreduces core the [7 blood,12,13]. flow Due to to the this peripheries vasoconstriction in favour and of a the central high pooling surface area-to-volumeof blood in the torso ratio, and the skindeep temperature body core [7,12,13]. of the extremities Due to this tends vasoconstric and exponentiallytion and the decreases high surface to a levelarea-to-volume approaching ratio, that the of the skin ambient temperature environment. of the extremities After a brief tends period and of exponentially lowered skin blood decreases flow andto a temperature,level approaching due to that the CIVC,of the aambient temporary environment. increase in After blood a flow brief and period rewarming of lowered occurs. skin During blood these flow and temperature, due to the CIVC, a temporary increase in blood flow and rewarming occurs. During episodes, skin temperature can rise by as much as 10 ◦C, and this fall and rise can occur repeatedly in a cyclicthese fashionepisodes, [7 ].skin This temperature pattern of periodiccan rise warmingby as much was as first 10 reported°C, and bythis Lewis fall and [14], rise who can labelled occur itrepeatedly the “hunting in a response”,cyclic fashion due [7]. to This its apparent pattern of oscillatory periodic warming pattern. Thiswas responsefirst reported is also by termedLewis [14], the cold-inducedwho labelled it vasodilation the “hunting (CIVD) response”, phenomenon due to its [15 apparent]. There oscillatory is a definite pattern. variation This in response the occurrence, is also magnitude,termed the andcold-induced duration ofvasodilation the CIVD[ 16(CIVD)]. phenomenon [15]. There is a definite variation in the occurrence,It was found magnitude, that the and CIVD duration occurs inof aboutthe CIVD 5 to 10[16]. min after the exposure of the hand to cold [15,17], and isIt initiatedwas found by thethat dilation the CIVD of theoccurs AVAs in [about7,13,15 5, 18to]. 10 Because min after ofthe the elevated exposure extremity of the hand blood to flowcold and[15,17], temperature, and is initiated CIVD hasby the generally dilation been of presumedthe AVAs to[7,13,15,18] provide a. protectiveBecause of function the elevated by maintaining extremity localblood tissue flow integrityand temperature, and minimizing CIVD has the generally risk of cold been injuries. presumed However, to provide the mechanisms a protective underlyingfunction by CIVDmaintaining are unclear, local tissue yet understanding integrity and minimizing the nature ofthe CIVD risk of is cold of important injuries. However, occupational the mechanisms and clinical relevanceunderlying [7 ].CIVD Additionally, are unclear, the yet review understanding studies of Cheung the nature et al. of [7CIVD,19] have is of shown important that itoccupational is not easy toand compare clinical direlevancefferent research [7]. Additionally, findings duethe review to the inconsistentstudies of Cheung methodologies et al. [7,19] in have the experimentalshown that it protocols,is not easy and to mostcompare of the different studies onresearch CIVD arefindings largely due descriptive, to the inconsistent lacking suffi cientmethodologies quantification in the of CIVDexperimental responses. protocols, and most of the studies on CIVD are largely descriptive, lacking sufficient quantification of CIVD responses. The current study was originated based on the findings of previous study by Youssef et. al. [20], in which the authors tried to take advantage of the CIVC reaction to prevent nail toxicity during Appl. Sci. 2019, 9, 3372 3 of 19

Appl. Sci.The 2019 current, 9, x FOR study PEER was REVIEW originated based on the findings of previous study by Youssef et. al.3 of [20 19], in which the authors tried to take advantage of the CIVC reaction to prevent nail toxicity during chemotherapy. DuringDuring theirtheir studystudy [[20],20], YoussefYoussef etet al.al. aimed to model the CIVC responses to localized cooling forfor the the purpose purpose of developingof developing a model-based a model-based controller controller of the fingerof the skin finger temperature. skin temperature. However, theHowever, developed the controllerdeveloped exhibited controller unpredictable exhibited unpredi disturbances,ctable representeddisturbances, by represented abrupt increases by abrupt in the skinincreases temperature in the skin due temperature to the CIVD due reaction. to the CIVD reaction. The mainmain goalgoal of of this this study study it toit tryto try to understandto understand and and quantify quantify the mechanism the mechanism of CIVC of CIVC and CIVD and byCIVD reverse by reverse engineering engineering the dynamic the dynamic responses responses of the hands’of the skinhands’ temperature skin temperature to localised to localised cooling usingcooling a databasedusing a databased mechanistic mechan (DBM)istic modelling (DBM) modelling approach. approach.

2. Materials and Methods

2.1. Controllable Active Cooling Device and Measurements (iGlove-1)(iGlove-1) An in-housein-house (University(University of Antwerp,Antwerp, Antwerp,Antwerp, Belgium)Belgium) developed active localisedlocalised coolingcooling device (iGlove-1iGlove-1, FigureFigure2 2))was was developed developed totoinvestigate investigate thethepossibility possibility ofoflocalised localised activeactivecooling cooling ofof hand fingersfingers [[21].21]. The iGlove-1 device was developed in such way as to provide a stable localised low temperaturetemperature (cooling)(cooling) toto thethe fivefive fingersfingers ofof thethe subject’ssubject’s leftleft hand.hand. The iGlove-1 was equipped with 20 Peltier elementselements (two(two elements elements positioned positioned on on both both sides sides of of each each finger) finger) to applyto apply localised localised cooling cooling of the of fingers. Each element had a size about 12 12 5 mm. the fingers. Each element had a size about× 12 ×× 12 × 5 mm.

Figure 2. The iGlove-1iGlove-1-controlled cooling devicedevice forfor thethe leftleft hand. (1) Peltier cooling elements; (2) NTC temperaturetemperature sensor to measure the fingerfinger skinskin temperature;temperature; (3) one probe of the blood flowflow Laser Doppler meter.

The iGlove-1 device consisted of a wooden construction on which the subject’s left hand can can rest. rest. The constructionconstruction was equippedequipped with fivefive mechanicallymechanically adjustable holders to ensure a goodgood contactcontact between the Peltier elements and the fingersfingers of didiffefferentrent handhand sizes.sizes. The two Peltier elements located on each side of the fingerfinger (two(two onon thethe fingertipfingertip andand anotheranother below the firstfirst phalanx,phalanx, Figure2 2)) werewere always electrically connectedconnected inin series.series. The iGlove-1iGlove-1 device was equippedequipped with fivefive NTCNTC sensorssensors (with(with anan accuracyaccuracy ofof ±0.10.1 ◦°C)C) to ± continuously measure the temperaturestemperatures ofof thethe left-handleft-hand fingers.fingers. Another 20 NTC sensors measured thethe temperaturetemperature ofof thethe PeltierPeltier elementselements (one(one sensorsensor forfor eacheach element).element). A Laser Doppler blood flowflow meter (MoorVMS-LDF2® byby Moor Moor Instruments) Instruments) was was used used to to measure measure the changes in the blood flowflow underneath thethe nail nail bed. bed. The The blood blood flow flow measurements measurements were were performed performed on only on only two fingers,two fingers, the index the fingerindex finger and the and thumb, the thumb, of the subject’sof the subject’s left hand left as hand a representation as a representation of the changes of the changes in the blood in the flow blood to theflow five to the fingers. five fingers. The temperaturetemperature sensorssensors werewere positioned positioned on on the the underside underside of of each each fingertip, fingertip, while while the the probes probes of theof the Laser-Doppler Laser-Doppler blood blood flow flow meter meter were were placed placed on on the the middle middle of of the the nails nails of ofthe the thumbthumb andand indexindex fingers.fingers. The skin temperatures of the five five fingersfingers andand that of the ambient air (in degrees Celsius, ◦°C)C) werewere recorded,recorded, asas wellwell as the blood flowflow (in Units, PU) of the thumb and the index finger, finger, every second (for moremore informationinformation seesee [[20–22]).20–22]).

2.2. Experiments Appl. Sci. 2019, 9, 3372 4 of 19

2.2. Experiments Data from two sets of experiments were used during the course of this work. The first set (Exp.1) was conducted during a previous study [20] with the objective of designing a model-based control system for localised cooling of hand termites to avoid nail toxicity during chemotherapy. The second set (Exp.2) of experiments was conducted during the course of this study to test the effect of intermittent cooling on the CIVD phenomena.

2.2.1. Test Subjects Data from two different sets of experiments (Table1) was obtained from 33 participants (test subjects). During the first set of experiments (Exp.1), a homogeneous group of 11 healthy women between the ages of 35 and 55 years performed the tests. This age range was chosen for the sake of the objective of the previous study [21], since a high incidence rate of breast cancer is recorded within this age range. The second set of experiments was performed using 12 test subjects, of which six were males and six were females with an age range between 18 and 24 years old.

Table 1. The number of test subjects participating in each of the conducted sets of experiments, showing the average-age and gender.

Gender Experiment Number of Participants Age MF Exp.1 11 44.9 ( 5.84) 0 11 ± Exp.2 12 20.4 ( 2.60) 6 6 ±

During the course of both sets (Exp.1 and Exp.2), all the test subjects were in healthy condition, non-smokers, having no hand injuries and with no evidence of the Perniosis or Raynaud phenomena. The absence of (excessive) alcohol consumption was ensured in all of the test subjects, starting from the evening (6–8 pm) before the test, with a normal (7–9) h of sleep during the night. During the two sets of experiments, all participants were asked to keep only light clothing (no jackets or pullovers) consisting of shirts (or sweaters) and pants (or skirts).

2.2.2. Experimental Protocol Acclimatisation stage: for both sets of experiments (Exp.1 and Exp.2), each test subject was seated at the start of the measurements in the test room for 30 min to acclimatise them to the continuously ± measured ambient air temperature (22.4 0.6 C) within the test room. ± ◦ Step experiment stage: after placing the subject’s left hand fingers in their appropriate positions on the iGlove-1 device (Figure2), for the first set of experiments, the set-point temperature on the controller of the Peltier elements was set to 20 ◦C for 15 min. For the next 30 min, a step-down decrease in the temperature of the Peltier element was applied by setting the controller set-point to 2 ◦C. These applied set-points were chosen in such way as to ensure that both the CIVC and CIVD phenomenon were triggered [20,21]. During the first set of experiments (Exp.1), for each test subject, the previous test protocol was repeated three times in three consecutive days at the same time of day, giving a total of 33 full experimental trials. The second set of experiments (Exp.2) consisted of two different phases (Figure3). Appl. Sci. 2019, 9, 3372 5 of 19 Appl. Sci. 2019, 9, x FOR PEER REVIEW 5 of 19

Figure 3. TheThe different different set temperature of the Peltier elements for for ( (AA)) experimental experimental phase phase (I) (I) and and ( (BB)) phase (II) of the second set of experiments.

During the first first experimental phase (I), the set- set-pointpoint temperature of the controller of the Peltier elements was set toto 2020 ◦°CC forfor 1515 min.min. ForFor thethe next next 60 60 min, min, a a step-down step-down decrease decrease in in the the temperature temperature of ofthe the Peltier Peltier element element was was applied applied by by setting setting the the controller controller set-point set-point to 2 to◦C. 2 °C. During During the the second second phase phase (II), (II),a a pulse train train (a rectangular (a rectangular pulse pulse wave) wave) of set of temperaturesset temperatures to the to the Peltier Peltier elements elements was was applied applied for for60 min.60 min. More More specifically, specifically, we set awe pulse set timea puls of 2e min,time a of minimum 2 min, anda mi maximumnimum and set temperaturesmaximum set of temperatures2 ◦C and 20 ◦C, of respectively2 °C and 20 °C, (see respectively Figure3B). (see Figure 3B). 2.3. System Identification and Modelling of CIVC/CIVD 2.3. System Identification and Modelling of CIVC/CIVD Although the system under study (the finger/blood circulation) is inherently a non-linear system, Although the system under study (the finger/blood circulation) is inherently a non-linear the essential perturbation behaviour can often be approximated well by simple linearized Transfer system, the essential perturbation behaviour can often be approximated well by simple linearized Function (TF) models [20,23–29]. Transfer Function (TF) models [20,23–29]. For the purposes of the present paper, the following linear, single-input, single-output (SISO) For the purposes of the present paper, the following linear, single-input, single-output (SISO) discrete-time transfer function (DTF) is considered [20], discrete-time transfer function (DTF) is considered [20], - 1+ +- m - B(z 1) y(k) =b1⋯z− ...bmz− u(k δ) + (k) = − u(k) + (k) yk 1+a- z 1+...+-a uzkn -δ ξk - Au(zkξ1) k𝑦𝑘 1⋯− n − − − (1) b z 1+ +b z m B(z 1) (1) ⋯1 − ... m − − y(k)= 1 n u(k δ) + ξ(k) = 1 u(k) + ξ(k) 1+a z +...+an𝑢z𝑘𝛿 𝜉𝑘 A(z𝑢𝑘) 𝜉𝑘 ⋯1 − − − − where y𝑦(k𝑘) is is thethe fingerfinger skinskin temperaturetemperature ((°C)◦C) and u𝑢𝑘(k) is is thethe temperaturetemperature ofof thethe PeltierPeltier elements 1 1 1 (°C),(◦C), while A𝐴(z𝑧− ) andandB 𝐵(z−𝑧 ) are are appropriately appropriately defined defined polynomials polynomials in thein the backshift backshift operator operatorz− ,𝑧 i.e.,, i.e.,z i y (𝑧k) =𝑦𝑘y(k𝑦𝑘𝑖i) and ξ (kand) is additive𝜉𝑘 is noise,additive a serially noise, uncorrelateda serially uncorrelated sequence of randomsequence variables of random with − − variablesvariance σ with2 that variance accounts 𝜎 for that measurement accounts noise,for measurement modelling errors noise, and modelling effects of unmeasurederrors and effects inputs of to unmeasuredthe process (assumed inputs to tothe be process a zero (assumed mean). For to convenience, be a zero mean). any For pure convenience, time delay ofanyδ >pure1 samples time delay can ofbe accounted𝛿1 samples for by can setting be accounted the δ 1 leading for byparameters setting the of 𝛿1 the B (leadingz 1) polynomial parameters to zero,of the i.e., 𝐵b𝑧,... − − 1 polynomial... , bδ 1 = 0. to zero, i.e., 𝑏, ……, 𝑏 = 0. − A step-input was applied, as ex explainedplained earlier, earlier, by suddenly dec decreasingreasing the temperature of the Peltier elements fromfrom 20 20 to to 2 ◦2C. °C. In In practice, practice, the the transition transition of the of inputthe input to the to new the steadynew steady state is state taking is takingsome time some (transition time (transition time). However, time). However, for convenience, for convenience, in this paper in thethis step-input paper the was step-input idealised was and idealisednormalised and by normalised assuming thatby assuming it starts from that zeroit starts and from changes zero instantaneously and changes instantaneously at a time equal at to a zero,time equal to zero, ( 0 f or t < 0 u(t) = 0 𝑓𝑜𝑟 𝑡 0 (2) 𝑢𝑡 1 f or t 0 (2) 1 𝑓𝑜𝑟≥ 𝑡 0 The Simplified Refined Instrumental Variable (SRIV) algorithm was utilised in the identification and estimation of the models (model parameters and model structure) [30,31]. Appl. Sci. 2019, 9, 3372 6 of 19

The Simplified Refined Instrumental Variable (SRIV) algorithm was utilised in the identification and estimation of the models (model parameters and model structure) [30,31]. Firstly, the appropriate model structure was identified, i.e., the most appropriate values for the triad [n, m, δ] (see Equation (1)), where n and m are the number of poles and zeros, respectively. Two main statistical measures were employed to determine the most appropriate values of this T triad. Namely, the coefficient of determination R2 , based on the response error; and YIC (Young’s Information Criterion), which provides a combined measure of model fit and parametric efficiency, with large negative values indicating a model that explains the output data well and yet avoids over-parameterisation [31,32].

3. Results and Discussion

3.1. System Identification

3.1.1. Data-Based Mechanistic Modelling of CIVC The measured blood flow, conducted during the first set of experiments (Exp.1), showed a decreasing pattern (average drop of 400 53 PU) coupled with decreased finger skin temperatures in ± response to the applied localized cooling (for more information see [20]). T In agreement with previous study [20], the SRIV algorithm combined with YIC and R2 suggested that a second-order (with number of poles n = 2 and zeros m = 2) discrete-time TF described the dynamic responses of finger skin temperature to step-decreases in the input (Peltier element’s temperature) most accurately (i.e., RT = 0.91 0.04 and YIC = 11.23 2.33) for all 33 test subjects. More specifically, 2 ± − ± the SRIV algorithm identified the following general discrete-time DTF model structure,

b z 1 + b z 2 y(k) = 1 − 2 − u(k δ) + ξ(k) (3) 1 2 1 + a1z− + a2z− − where the pure time delay (δ) was different from test subject to another (interpersonal variation) with an average (δ = 2.3 min) and standard deviation (SD = 1). The variations in the time delay of the model reflects the different individual biological responses to colder environment. Figure4 shows a simulation example of the resulting model (3), showing the simulated dynamic responses of the finger Appl.skin Sci. temperature2019, 9, x FOR PEER to step REVIEW decrease (cooling) in the Peltier element temperature. 6 of 20

190 191 FigureFigure 4. A 4. simulationA simulation example example of the of thesecond-order second-order DTF DTF (3) (3)that that represents represents the the finger’s finger’s temperature temperature 192 responseresponse (CIVC (CIVC reaction) reaction) to step to the decrease step decrease in Peltier inPeltier element element temperature temperature (cooling). (cooling).

193 194 In order to understand the underlying mechanism of the resulted second-order system (3), 195 describing the CIVC process, it was decomposed into simpler two first-order transfer functions (TF). 196 These two first-order TFs can be interconnected by the three well-known configurations, namely 197 series, parallel and feedback configurations. The results showed that the parallel configuration 198 (Figure 5) was mathematically most suitable (average 𝑅 = 0.91± 0.01) to describe the dynamic 199 response of the CIVC process in all test subjects. As depicted in Figure 5, the second-order system (3), 200 representing the CIVC process, was decomposed into the two first-order TFs defined as follows: 201 𝑇𝐹 = , 202 𝑇𝐹 = , 203 𝑦(𝑘) = 𝑇𝐹 +𝑇𝐹.𝑢(𝑘−𝛿) (4) 204

205 206 Figure 5. The parallel configuration of the interconnection between the two first-order TFs resulted 207 from the decomposition of the second-order system (Eq.3).

208 The time constants 𝜏 and 𝜏 of 𝑇𝐹 and 𝑇𝐹, respectively, were calculated and compared for 209 all test subjects, where 𝜏=1/ln (−𝑎). Table 1 shows the mean and standard deviation of the 210 calculated time constants obtained from all test-subjects during the two sets of experiments (Exp1 211 and Exp2.Phase 1). 212

213 Table 1. Mean and standard deviation of the calculated time constants, of the decomposed two first- 214 order TF, obtained from all test subjects (33) during the two sets of experiments (Exp1 and Exp.2- 215 Phase1). Appl. Sci. 2019, 9, 3372 7 of 19

Appl. Sci.To 2019 understand, 9, x FOR PEER the REVIEW underlying mechanism of the resulting second-order system (3), describing7 of 19 the CIVC process, it was decomposed into two simpler first-order transfer functions (TF). These two first-orderfirst-order TFs TFs can can be be interconnected interconnected in inthree three well-known well-known configurations, configurations, namely, namely, series, series, parallel parallel and feedbackand feedback configurations. configurations. The Theresults results showed showed that that the theparallel parallel configuration configuration (Figure (Figure 5)5) waswas mathematicallymathematically most most suitable suitable (average (average 𝑅RT = 0.91 ± 0.01)0.01) for for describing describing the the dynamic dynamic response response of of the the 2 ± CIVCCIVC process process in all testtest subjects.subjects. AsAs depicteddepicted in in Figure Figure5, 5, the the second-order second-order system system (3), (3), representing representing the theCIVC CIVC process, process, was was decomposed decomposed into into two two first-order first-order TFs, TFs, defined defined as follows: as follows:

𝑏 𝑇𝐹 b1 TF = 1 1𝑎𝑧 1 1 + a1z−

𝑏 𝑇𝐹 b2 TF2 = 1𝑎𝑧 1 1 + a2z−

y(k) = [TF1 + TF2] u(k δ) (4) 𝑦𝑘 𝑇𝐹 𝑇𝐹.𝑢𝑘𝛿· − (4)

FigureFigure 5. 5. TheThe parallel parallel configuration configuration of of the the interconnection interconnection between between the the two two first-order first-order TFs TFs resulting resulting fromfrom the the decomposition decomposition of of the the seco second-ordernd-order system system (Equation (Equation (3)). (3)).

TheThe time time constants constants 𝜏τ1 and τ𝜏2 ofofTF 𝑇𝐹1 and andTF 𝑇𝐹2, respectively,, respectively, were were calculated calculated and and compared compared for for all alltest test subjects, subjects, where whereτ = 1𝜏1/ln/ ln ( a) .𝑎 Table. Table2 shows 2 shows the mean the and mean standard and standard deviation deviation of the calculated of the − calculatedtime constants time obtainedconstants fromobtained all test-subjects from all test-sub duringjects the during two sets the of two experiments sets of experiments (Exp.1 and (Exp.1 Exp.2, andPhase Exp.2, I). Phase I ).

TableTable 2. 2. MeanMean and and standard standard deviation deviation of the of thecalculated calculated time time constants, constants, of the of decomposed the decomposed two first- two orderfirst-order TF, obtained TF, obtained from from all test all testsubjects subjects (33) (33) during during the the two two sets sets of ofexperiments experiments (Exp.1 (Exp.1 and and Exp.2, Exp.2, PhasePhase I I).). ( ) ( ) 𝝉𝟏 (min)τ1 min τ2 min𝝉𝟐 (min) Mean Mean7.34 7.34 0.73 0.73 Standard deviationStandard deviation 3.2 3.2 0.56 0.56

TheThe aforementioned aforementioned results results suggested suggested two two parallel parallel underlying underlying processes processes ta takingking place place during during the the CIVCCIVC action. action. However, However, by by comparing comparing the the calculated calculated time time constants, constants, it it became became clear clear that that the the process process representedrepresented by TF𝑇𝐹 was,was, on on average, average, 10 10 times times faster faster (τ (𝜏0.73 min)0.73 min) than thethan one the represented one represented by TF by(τ 2 2 ≈ 1 1 𝑇𝐹7.34 (𝜏 min). 7.34 min). ≈ PhysicalPhysical and and physiological physiological insights insights into into the the re resultingsulting mathematical mathematical model model were were investigated investigated usingusing first first principles principles (e.g., (e.g., Fourier’s Fourier’s law law and and Newton’s Newton’s law law of of cooling) cooling) and and other other mechanistic mechanistic models models (e.g.,(e.g., [12]). [12]). TheThe heat flowflow throughthrough any any object, object, including including the finger,the finger, can becan described be described conventionally conventionally by lumped by lumpedquantities quantities such as thermalsuch as thermal resistance resistance (or conductance) (or conductance) and thermal and thermal capacitance capacitance [27]. The [27]. heat The balance heat balance equation representing the heat flow (W) between the finger and the colder Peltier’s element can be given by:

𝑑𝑇 ℎ𝐴 ℎ𝐴 𝐾𝐴 𝑇 𝑇 𝑇 𝑇 𝑇 𝑇 (5) 𝑑𝑡 𝐶 𝐶 𝐶 Appl. Sci. 2019, 9, 3372 8 of 19 equation representing the heat flow (W) between the finger and the colder Peltier’s element can be given by: ( ) dTskin hveinAvein hcapAcap KskinAskin Appl. Sci. 2019, 9, x FOR= PEER REVIEW(Tbld Tskin)+ (Tbld Tskin) (Tskin T ) 8 of(5) 19 dt Cskin − Cskin − − Cskin − ∞

−1 where 𝐶 (J.°C ) is the skin thermal capacitance, 𝑇 is the finger skin temperature, ℎ (W where C (J. C 1) is the skin thermal capacitance, T is the finger skin temperature, −2 −1 skin ◦ − skin 𝐴 m °C ) is 2the convictive1 heat transfer coefficient of flowing blood in the superficial vein, is hvein (W m− ◦C− ) is the convictive heat transfer coefficient of flowing blood in the−2 superficial−1 the cross-section area of the superficial vein, 𝑇 is the blood temperature, ℎ (W m °C ) is the vein, A is the cross-section area of the superficial vein, T is the blood temperature, h (W m 2 convectivevein heat transfer coefficient of the blood in the superficialbld capillaries network, 𝐾 cap (W m−−2 C 1) is the convective heat transfer coefficient of the blood in the superficial capillaries network, ◦°C−1) is the skin conductance. K (W m 2 C 1) is the skin conductance. skin Under− normal◦ − temperature (normothermia), before applying the step cooling using the Peltier’s Under normal temperature (normothermia), before applying the step cooling using the Peltier’s element, there is a baseline level of vasoconstrictive tone [33], where the blood velocity fluctuates, element, there is a baseline level of vasoconstrictive tone [33], where the blood velocity fluctuates, between a high level and a very low level, with about 2–3 vasoconstrictions per minute [17]. The high between a high level and a very low level, with about 2–3 vasoconstrictions per minute [17]. The level corresponds to a state when the AVAs were open. However, when the local environmental high level corresponds to a state when the AVAs were open. However, when the local environmental temperature (Peltier’s element temperature) drops, the AVAs close, causing the direct blood flow temperature (Peltier’s element temperature) drops, the AVAs close, causing the direct blood flow from the to the superficial vein to stop quite abruptly. Hence, the convective heat transfer from the artery to the superficial vein to stop quite abruptly. Hence, the convective heat transfer ( .𝑄 ℎ𝐴𝑇 𝑇 ) from the blood in the superficial veins (Figure 6) decreases (Q = h A (T T )) from the blood in the superficial veins (Figure6) decreases dramatically, dramatically,vein vein veincausingbld −a fastskin reduction in the skin temperature, which can be represented by the causing a fast reduction in the skin temperature, which can be represented by the transfer function transfer function 𝑇𝐹 . On the other hand, the convective heat. transfer from capillaries TF𝑄2. Onℎ the other𝐴 hand,𝑇 the𝑇 convective heat transfer from capillaries (Qcap = hcapAcap(Tblood 𝑄T skin)) ( ) together .with the conductive heat exchange ( − together 𝐾𝐴 with𝑇 the𝑇 conductive) between heat the exchange skin and (colderQskin = Peltier’sKskinA elementskin(Tskin areT dissipating)) between the the heat skin much and − ∞ colderslower. Peltier’s This is elementmainly due are dissipatingto the effect the of heatskin muchthermal slower. capacitance This is mainlyand the due high to theresistance effect of of skin the thermalcapillaries capacitance to blood andflow. the Hence, high resistance TF1, with of the the capillariesslow time toconstant, blood flow. is suitable Hence, TF1,for describing with the slow the timedynamic constant, response is suitable of both for the describing convective the heat dynamic transfer response from capillaries of both the and convective conductive heat heat transfer exchange from capillariesbetween the and skin conductive and the Peltier’s heat exchange element. between the skin and the Peltier’s element.

FigureFigure 6.6. Schematic representation of the heat transfertransfer between the fingerfinger andand thethe PeltierPeltier elementelement throughthrough threethree di differentfferent layers, layers, namely, namely, deep deep skin skin layer, layer, surface surface skin skin layer layer and and the Peltier’sthe Peltier’s element. element. The AVAThe AVA controls controls the direct the direct flow betweenflow betw theeen artery the artery and the and surface the surface vein. vein.

3.1.2.3.1.2. Data-Based Mechanistic Modelling ofof CIVDCIVD AmongAmong thethe 3333 testtest subjects,subjects, 27 showed the huntinghunting reaction with cycles of CIVC and CIVD. FigureFigure7 7 shows shows an an example example of of the the resulting resulting hunting hunting reaction reaction to to continuous continuous localised localised cooling cooling using using Peltier’sPeltier’s element temperature atat 22 ◦°C.C. Appl. Sci. 2019, 9, x FOR PEER REVIEW 8 of 20

250 251 Figure 6. [A] Vascular system in the skin (adapted from [37]) [B] Schematic representation of the heat 252 transfer between the finger and the Peltier element through three different layers, namely deep skin 253 layer, surface skin layer and the Peltier’s element. The AVA is controlling the direct flow between the 254 artery and the surface vein [13].

255 3.1.2. Data-based mechanistic modelling of CIVD 256 From all the 33 test subjects, 27 showed the hunting reaction with cycles of CIVC and CIVD. Appl. Sci. 2019, 9, 3372 9 of 19 257 Figure 7 is showing an example of the resulting hunting reaction to continuous localised cooling 258 using Peltier’s element temperature at 2 oC.

259 260 FigureFigure 7. 7.DynamicDynamic response response ofof fingerfinger's skin skin temperature temperature to step to decrease step decrease in Peltier’s in elementPeltier's temperature element

261 temperaturefrom 20 ◦C from to 2 ◦20C, °C showing to 2 °C, an showing example an of exampl the huntinge of the reaction hunting in reaction a test subject. in a test subject.

262 WithinWithin the the cooling cooling period period of of60min, 60 min, all alltest test su subjectsbjects, exhibiting exhibiting hunting hunting reactions, reactions have showed shown three 263 threeconsecutive consecutive cycles cycles of CIVC of CIVC/CIVD/CIVD (an (example example isis shownshownin inFigure Figure7 ).7). 264 A Asecond-order second-order DTF DTF with with two two poles poles (𝑛 ( =n 2)= 2)and and two two zeroes zeroes (𝑚 ( m = 2)= 2)was was the the best best model model structure structure 265 (with(with average average 𝑅R T= =0.920.92 ±0.040.04 and and 𝑌𝐼𝐶YIC = =− 10.6110.61 ±3.45)3.45) to todescribe describe the the CIVD CIVD response response to tolocalised localised 2 ± − ± 266 coolingcooling for for all all test test subjects subjects with with hunting the hunting reaction: reaction: 267 𝑦(𝑘) = 𝑢(𝑘−𝛿) + (𝑘) 1 2 (6) b z + b z y(k) = 1 − 2 − u(k δ) + ξ(k) (6) 268 The structure of the identified model, represented1 2by the triad [𝑛=2, 𝑚=2, 𝛿], have shown an 1 + a1z− + a2z− − 269 average time delays 𝛿 of 10.23min (±3.50min). In other words, for all test subjects that have shown 270 the huntingThe structure reaction,of the the first identified episode model, of CIVD represented started, on by average, the triad after [n = 10.232, m = ±3.50min2, δ], showed from anthe average start time delay δ of 10.23 min ( 3.50 min). In other words, for all test subjects that showing the hunting ± reaction, the first episode of CIVD started, on average, after 10.23 3.50 min from the start of applying ± the localised cooling. Table3 shows the estimation results of the identified model (6) for all test subjects showing the hunting reaction.

T Table 3. Average and standard deviation of parameter estimates, R2 and YIC of the second-order DTF model describing the CIVD reaction to continuous localised cooling experiments obtained from the test-subjects that shown hunting reaction (i.e., cycles of CIVC/CIVD episodes).

1 1 A(z− ) B(z− ) 2 δ (min) RT YIC a1 a2 b0 b1 b2 1.989 0.980 0.0 0.0047 0.0045 10.23 0.92 10.61 − − − 0.005 0.002 0.0 0.0010 0.0010 3.50 0.04 3.45 ± ± ± ± ± ± ± ±

This relatively long time delay, compared to the CIVC case, was somehow misleading in terms of system causality, since during this lag of time between the cause (step cooling) and the modelled effect (CIVD), there was another effect, namely the CIVC. Therefore, the model input, represented by the step decrease in the Peltier’s element temperature, cannot fully explain the CIVD effect. However, the . rate of heat dissipation (Q , Watt), from the finger to the Peltier’s elements, shows more dynamics in dis . relation to both CIVC and CIVD. The heat dissipation rate (Qdis) is calculated based on Newton’s law of cooling as follows [34]: . Qdis = hPAP(Tsk T ) (7) − − ∞ Appl. Sci. 2019, 9, x FOR PEER REVIEW 10 of 19

−2 where ℎ is the heat transfer coefficient between the finger’s skin and Peltier’s element (=15 W m −1 °C , from the datasheet of the Peltier’s element) and 𝐴 is the total surface area of the Peltier’s elements in contact with the skin (=5.76 × 10−4 m2). An example of the simulated finger skin temperature during the CIVD reaction using the identified second-order DTF (6) is shown in Figure 8. Additionally, Figure 8 shows the calculated Appl.dissipated Sci. 2019 ,heat9, 3372 rate (𝑄) using Equation (7), while the area-under-the-curve represents the amount10 of 19 of the dissipated heat (𝑄, Joules) from the finger to the Peltier’s elements. The results showed that the average amount of dissipated heat from the skin of the finger before 2 wherethe CIVDhP is kick-off the heat (termed transfer here coe asffi latentcient betweenheat for CIVD the finger’sor LH-CIVD) skin and is 102.10 Peltier’s (±22.36) element joules. (=15 We W found m− 1 ◦thatC− ,there from was the datasheeta significant of thedifference Peltier’s between element) the and testA subjectsP is the total(interpersonal) surface area that of exhibited the Peltier’s the elements in contact with the skin (=5.76 10 4 m2). hunting effect with respect to their latent× heat− for CIVD (LH-CIVD), and this at a significance level of 1%. AnIn other example words, of the the simulated LH-CIVD finger can skin be temperatureconsidered an during individual-depende the CIVD reactionnt usingcharacteristic. the identified The second-order DTF (6) is shown in Figure8. Additionally, Figure8 shows the calculated dissipated heat proposed. LH-CIVD term combined three main factors that are believed to affect the thermostatic rateresponses, (Qdis) using namely, Equation the rate (7), of while cooling the [35], area-under-the-curve the temperature to represents which the the skin amount is cooled of the [36], dissipated and the heatduration (Qdis ,of Joules) exposure from [37]. the finger to the Peltier’s elements.

FigureFigure 8.8. Measured and simulatedsimulated fingerfinger skinskin temperaturetemperature duringduring thethe CIVDCIVD (upper(upper graph),graph), thethe dissipateddissipated heatheat raterate fromfrom thethe fingerfinger andand thethe area-under-the-curvearea-under-the-curve representsrepresents thethe amountamount ofof dissipateddissipated heatheat inin joulesjoules (lower(lower graph).graph).

TheThe resultssecond-order showed TF that (6) thedescribing average the amount CIVD of re dissipatedaction was heat decomposed from the skininto oftwo the first-order finger before TFs thewith CIVD a parallel kick-o configurationff (termed here (the as samelatent as heatdescribed for CIVD in Figureor LH-CIVD) 5) as the ismost 102.10 mathematically ( 22.36) joules. suitable We ± foundconfiguration that there (average was a significant 𝑅 = 0.93 di± ff0.01).erence The between resulting the time test subjectsconstants (interpersonal) 𝜏 and 𝜏 of that𝑇𝐹 exhibitedand 𝑇𝐹, therespectively, hunting e ffwereect with calculated respect and to theircompared latent heatfor all for test CIVD subjects (LH-CIVD), exhibiting and the this CIVD at a significancereaction, as levelshown of in 1%. Table In other 4. words, the LH-CIVD can be considered an individual-dependent characteristic. The proposed LH-CIVD term combined three main factors that are believed to affect the thermostatic responses,Table namely,4. Mean and the standard rate of cooling deviation [35 of], the the calculated temperature time toconstants, which theof the skin decomposed is cooled two [36], first- and the durationorder of TF, exposure obtained [ 37from]. all test subjects with CIVD reaction during the two sets of experiments (Exp.1 Theand second-orderExp.2, Phase I). TF (6) describing the CIVD reaction was decomposed into two first-order TFs with a parallel configuration (the same as described in Figure5) as the most mathematically suitable 𝝉𝟏 (min) 𝝉𝟐 (min) configuration (average RT = 0.93 0.01). The resulting time constants τ and τ of TF and TF , 2Mean ± 7.96 10.81 2 1 2 respectively, were calculated and compared for all test subjects exhibiting the CIVD reaction, as shown Standard deviation 4.35 0.65 in Table4.

TableIn the 4. sameMean fashion and standard as with deviation the CIVC of thereaction, calculated the timecalculated constants, time of constants the decomposed suggested two two parallelfirst-order responses TF, obtained with clear from and all test different subjects dynamics. with CIVD reactionThe first during response, the two represented sets of experiments by the first- order(Exp.1 model and 𝑇𝐹 Exp.2,, was Phase slow I). (𝜏 7.96 min) in comparison to that represented by the first-order 𝑇𝐹

τ1 (min) τ2 (min) Mean 7.96 0.81 Standard deviation 4.35 0.65 Appl. Sci. 2019, 9, x FOR PEER REVIEW 11 of 19

(𝜏 0.81 min). The fast response can be attributed to the gradual opening of the AVAs during the CIVD.

The time constants, 𝜏 and 𝜏 , for the CIVC and CIVD responses were compared by the Kruskal-Wallis test. It was found that there was no significant difference, at a significance level of 1%,

in the first time constant (𝜏) for both CIVC and CIVD. The same results were noticed for the second time constant (𝜏). Appl. Sci. 2019, 9, 3372 11 of 19 3.1.3. Modelling of Localized Intermittent Cooling Effect

InDuring the same the fashionlocalised as intermittent with the CIVC cooling reaction, (Exp.2, the calculated Phase II), timenone constants of the test suggested subjects that two parallelshowed responsesthe hunting with reaction clear and (CIVC/CIVD different dynamics. cycles) during The first the response, continuous represented cooling by (Phase the first-order I) showed model any TFepisodes, was slowof CIVD. (τ On7.96 the min) other in comparisonhand, intermittent to that representedcooling induced by the an first-order episode ofTF CIVC,(τ causing0.81 min). the 1 1 ≈ 2 1 ≈ Thefinger’s fast responsetemperature can to be drop attributed to the tosame the graduallevel reac openinghed during of the continuous AVAs during cool theing CIVD.(on average, 16.2 ± 0.7 °C) and continued until the end of the experiment. Figure 9 shows an example of the finger’s The time constants, τ1 and τ2, for the CIVC and CIVD responses were compared by the Kruskal-Wallistemperature response test. It to was intermittent found that cooling. there Ad wasditionally, no significant a second-order difference, (with at a number significance of poles level 𝑛 = 2 and zeros 𝑚 = 2) discrete-time TF described the dynamic responses of finger skin temperature of 1%, in the first time constant (τ1) for both CIVC and CIVD. The same results were noticed for the (CIVC) to a series of cooling (intermittent cooling) in the input (Peltier element’s temperature) second time constant (τ2). most accurately (i.e., 𝑅 = 0.92 ± 0.02 and 𝑌𝐼𝐶 = −11.67 ± 3.55) with same structure as the TF 3.1.3.represented Modelling by (3). of Localized Table 5 show Intermittents the resulting Cooling average Effect parameter estimates and delays from the identified DTF model describing the CIVC reaction to intermittent cooling. During the localised intermittent cooling (Exp.2, Phase II), none of the test subjects that showed the hunting reaction (CIVC/CIVD cycles) during the continuous cooling (Phase I) showed any episodes Table 5. Average and standard deviation of parameter estimates, 𝑅 and 𝑌𝐼𝐶 of the identified of CIVD. On the other hand, intermittent cooling induced an episode of CIVC, causing the finger’s second-order DTF model describing the CIVC reaction to the localised intermittent cooling temperature to drop to the same level reached during continuous cooling (on average, 16.2 0.7 C) experiment (Exp.2, Phase II). ± ◦ and continued until the end of the experiment. Figure9 shows an example of the finger’s temperature response to intermittent cooling. Additionally, a second-order (with number of poles n = 2 and zeros 𝑨𝒛𝟏 𝑩𝒛𝟏 𝟐 m = 2) discrete-time TF described the dynamic responses of finger𝜹 (min) skin temperature𝑹𝑻 𝒀𝑰𝑪 (CIVC) to a series of cooling pulses𝒂𝟏 (intermittent 𝒂𝟐 cooling)𝒃𝟎 in the𝒃𝟏 input (Peltier𝒃𝟐 element’s temperature) most accurately (i.e., RT = 0.92 0.02 and YIC = 11.67 3.55) with same structure as the TF represented by (3). Table5 2 ± − ± shows the resulting−1.987 average 0.987 parameter 0.0 estimates−0.0016 and delays0.0018 from 2.34 the identified 0.92 DTF−11.67 model describing the CIVC reaction± 0.006 to intermittent± 0.001 cooling.± 0.0 ± 0.0010 ± 0.0010 ±1.21 ± 0.02 ± 3.55

FigureFigure 9.9. TheThe dynamic dynamic response response (upper (upper graph) graph) of the of thefinger finger’s’s temperature temperature (CIVC) (CIVC) to a series to a seriesof pulses of pulsesin Peltier’s in Peltier’s element element temperature temperature (middle (middle graph) graph).. Showing Showing the the measured measured and and simulated finger’sfinger’s temperaturetemperature (upper(upper graph) graph) using using a a second-order second-order DTF DTF and and the the model model residuals residuals (lower (lower graph). graph). Appl. Sci. 2019, 9, 3372 12 of 19

T Table 5. Average and standard deviation of parameter estimates, R2 and YIC of the identified second-order DTF model describing the CIVC reaction to the localised intermittent cooling experiment (Exp.2, Phase II).

1 1 A(z− ) B(z− ) 2 δ (min) RT YIC a1 a2 b0 b1 b2 1.987 0.987 0.0 0.0016 0.0018 2.34 0.92 11.67 − − − 0.006 0.001 0.0 0.0010 0.0010 1.21 0.02 3.55 ± ± ± ± ± ± ± ±

Although the finger skin temperature, under intermittent cooling, reached the same level (on average, 16.2 0.7 C) as that under continuous cooling, the intermittent cooling did not induce ± ◦ reheating of the fingers (i.e., CIVD). This indicates that the temperature to which the skin was cooled is not the only triggering factor for the CIVD. Additionally, it was clear that the vasodilation here (CIVD) is typically transient, which may interrupt the original vasoconstriction. The current work suggests that the rate at which the skin was cooled (rate of dissipated heat from the skin) is one of the main triggering factors, aside from the skin temperature and the duration of cooling [7,15,19,38]. The results showed that all test subjects exhibited the hunting reaction (i.e., episodes of CIVD occurred) during . dQdis continuous cooling (Exp.2, phase I), when the rate of change in the dissipated heat from skin ( dt ) was quasi zero (an example from one test subject is shown in Figure 10). On the other hand, for the . dQdis same test subjects, under intermittent cooling (Exp.2, Phase II) the rate of change ( dt ) oscillated around zero ( 0.0016), and no evidence of vasodilation was noticed (an example from one test subject ± is shown in Figure 11). Appl. Sci. 2019, 9, x FOR PEER REVIEW 12 of 20

357 . 358 FigureFigure 10. 10.DynamicDynamic response response of finger’s of finger skin skin temperature temperature (upper (upper graph), graph), dissipated dissipated heat heat rate rate (𝑄 (Q, , . dis 359 middle graph) and first derivative of the dissipated heat ratedQdis ( , lower graph) to localised middle graph), and first derivative of the dissipated heat rate ( dt , lower graph) to localised continuous 360 continuouscooling obtained cooling obtained from test from subject test (s5) subject during (s5) the during experiment experiment (Exp.2, (Exp.2-phaseI). Phase I).

361

362

363 Figure 11. Dynamic response of finger’s skin temperature (upper graph), dissipated heat rate (𝑄, 364 middle graph) and first derivative of the dissipated heat rate ( , lower graph) to localised 365 intermittent cooling obtained from test subject (s5) during experiment (Exp.2-phaseII).

366 The following section of this paper explores the different theories and mechanisms explaining 367 the thermoregulatory CIVC/CIVD reactions.

368 3.2. Physiological/mechanistic interpretation of thermoregulatory CIVC/CIVD reactions

369 3.2.1. Mechanisms of CIVC/CIVD reactions during localized cooling 370 The initial response to cold exposure is a sympathetically-mediated peripheral vasoconstriction, 371 resulting in reduced local tissue temperature [14], [18], [43], [44]. With continued cold exposure, this 372 vasoconstriction may be interrupted, resulting in periods of vasodilation, which correspond to an 373 increase in tissue temperature [45]. The local cooling vasoconstrictor response is dependent on intact Appl. Sci. 2019, 9, x FOR PEER REVIEW 12 of 20

357

358 Figure 10. Dynamic response of finger’s skin temperature (upper graph), dissipated heat rate (𝑄, 359 middle graph) and first derivative of the dissipated heat rate ( , lower graph) to localised 360 Appl.continuous Sci. 2019, 9 cooling, 3372 obtained from test subject (s5) during experiment (Exp.2-phaseI). 13 of 19

361

362 . 363 FigureFigure 11. 11.DynamicDynamic response response of finger’s of finger skin skin temperature temperature (upper (upper graph), graph), dissipated dissipated heat heat rate rate (𝑄 (Q, , . dis dQ 364 middlemiddle graph) graph), and and first first derivative ofof the the dissipated dissipated heat heat rate (ratedis ,( lower , graph)lower tograph) localised to intermittentlocalised dt 365 intermittentcooling obtained cooling fromobtained test subjectfrom test (s5) subject during (s5) the during experiment experiment (Exp.2, (Exp.2-phaseII). Phase II).

366 TheThe following following section section of of this this paper paper explores explores th thee different different theories andand mechanismsmechanisms explainingexplaining the 367 thethermoregulatory thermoregulatory CIVC CIVC/CIVD/CIVD reactions. reactions. 3.2. Physiological/Mechanistic Interpretation of Thermoregulatory CIVC/CIVD Reactions 368 3.2. Physiological/mechanistic interpretation of thermoregulatory CIVC/CIVD reactions 3.2.1. Mechanisms of CIVC/CIVD Reactions during Localised Cooling 369 3.2.1. Mechanisms of CIVC/CIVD reactions during localized cooling The initial response to cold exposure is a sympathetically mediated peripheral vasoconstriction, 370 The initial response to cold exposure is a sympathetically-mediated peripheral vasoconstriction, resulting in reduced local tissue temperature [11,15,39,40]. With continued cold exposure, this 371 resulting in reduced local tissue temperature [14], [18], [43], [44]. With continued cold exposure, this vasoconstriction may be interrupted, resulting in periods of vasodilation, which correspond to an 372 vasoconstriction may be interrupted, resulting in periods of vasodilation, which correspond to an increase in tissue temperature [41]. The local cooling vasoconstrictor response is dependent on intact 373 increase in tissue temperature [45]. The local cooling vasoconstrictor response is dependent on intact noradrenergic cutaneous active vasoconstrictor nerves [36,39,42]. Johnson et al. [36] concluded in their work that local cooling of skin occurs in two phases (biphasic): an initial phase, which lasts for few minutes (in accordance to the aforementioned results) and a prolonged phase. The initial phase is mediated by activation of cold-sensitive afferent neurons that affect the release of from sympathetic cutaneous vasoconstrictor nerves. Norepinephrine then vasoconstricts skin vessels (mainly the AVAs, in this case) through post-junctional α-receptors. On the other hand, the mechanisms for the prolonged phase, which follows an initial CIVD (hunting reaction), are suggested to be non-neurogenic [36], because no manipulations altered the prolonged cutaneous vasoconstriction during prolonged local cooling. However, these mechanisms have not been defined further [36]. Additionally, prolonged local cooling also mediates an initial “non-neurogenic” vasodilation (CIVD) that competes with the initial noradrenergically mediated vasoconstriction. Several hypotheses have been postulated on the mechanism of CIVD [15]. The main hypotheses to explain the initial CIVD and prolonged CIVC are depicted in Figure 12. In the case of prolonged localised cooling, and after an initial episode of CIVC (Figure 12A), an initial CIVD might occur. Based on previous research work (e.g., [15,18,43,44]), three different mechanisms are suggested to explain this initial CIVD (Figure 12). The first hypothesized mechanism (pathway 1) states that the smooth muscles in the blood-vessel walls become paralysed, for example, by a decreased concentration of Ca2+ ions. Consequently, the paralysed smooth muscles will not be able to maintain vasoconstriction, and then vasodilation occurs. The second hypothesized mechanism (pathway 2) states that the smooth muscles become less sensitive to norepinephrine, for example, due to the resorption of the receptors from the cell membrane. The Appl. Sci. 2019, 9, 3372 14 of 19 more resorption, the less norepinephrine can interact, the less the increase in intracellular Ca2+ ion concentration, and the less the constriction. The third and final hypothesized mechanism (pathway 3) states that the adrenergic vasoconstrictor nerves release less norepinephrine. Thereby, the concentration of in the synaptic cleft decreases. The bound epinephrine will detach from the receptors

Appl.due toSci. the 2019 concentration, 9, x FOR PEER REVIEW difference (diffusion), resulting in vasodilation. 14 of 19

Figure 12. MainMain hypotheses hypotheses explaining explaining the hunting reaction (with pathways 1,2 and 3 representing the three proposed hypotheses fromfrom literatureliterature toto explainexplain thethe initialinitial CIVD).CIVD).

3.2.2.The A New findings Model of for the Thermoregulatory current study do not Localised support CIVC/CIVD the first hypothesis Reactions (pathway 1), since it is clear from the case of intermittent localised cooling that the skin was cooled to the same temperature as in In the present paper, we suggest a new model for thermoregulatory localised CIVC/CIVD case of continuous cooling and yet no vasodilation evidence is recorded. reactions. Figure 13 depicts the main workflow of the suggested CIVC/CIVD thermoregulatory In agreement with the work of Yamazaki et al. [35], the present study suggests that the triggering model. The proposed model is based on the suggestion that there have to be rate-sensitive receptors, of local cooling induced-vasodilation in the finger’s skin is dependent on the heat dissipation rate which. are able to detect the changes in the heat dissipation rate (Q ). This rate-sensitive mechanism, (Q ) or the rate of cooling as termed in [35,38]. whichdis is not yet clear, is also suggested by Yamazaki et al. [35]. It is clear from the current work and Although the aforementioned hypotheses suggest non-neurogenic CIVD mechanisms, it is the presented results by Youssef et al. [20] that the CIVC, indicated by drop in blood flow rate (320 ± undisputed that CIVD magnitude and onset time are strongly dependent on central factors and 92 PU), starts earlier (1.55 ± 21 min), before the drop in the skin temperature. This suggests that the sympathetic activity [45–48]. Mekjavic et al. [49] showed that after 13 days of immersing one hand, for initial CIVC is triggered not based on skin temperature threshold, but rather on a certain threshold 30 min daily, in 8 C water, both the acclimated and contralateral (non-acclimated) hand decreased in the rate of heat◦ dissipation from the skin to the surrounding environment. Under normal temperature (normothermia), the blood vessels are dilated (initial state = vasodilation), with a baseline level of vasoconstrcitive tone [33]. Due to the temperature difference ∆𝑇 𝑇 𝑇 between skin and the environment, which is the driving force for heat flow, there is always a certain level of negative heat flux (dissipation) from the skin to the surrounding environment. Once the step- localised cooling is applied, this results in a sudden increase in the temperature difference ∆𝑇 = 18 ± 0.6 °C in the first two minutes), and consequently, a sudden increase in the heat dissipation rate

(Q = −0.15 ± 0.2 W in the first two minutes). If this change in the heat dissipation rate is above a certain threshold, the CIVC mechanisms are activated and vasoconstriction prevailed. Then, if the Appl. Sci. 2019, 9, 3372 15 of 19

CIVD frequency and finger temperatures. Such observations resulted in an additional central model explaining CIVD, wherein the release of peripheral vasoconstriction serves to release excess heat from the body assuming sufficient body heat content in the core.

3.2.2. A New Model for Thermoregulatory Localised CIVC/CIVD Reactions In the present paper, we suggest a new model for thermoregulatory localised CIVC/CIVD reactions. Figure 13 depicts the main workflow of the suggested CIVC/CIVD thermoregulatory model. The proposed model is based on the suggestion that there have to be rate-sensitive receptors, which are . able to detect the changes in the heat dissipation rate (Qdis). This rate-sensitive mechanism, which is not yet clear, is also suggested by Yamazaki et al. [35]. It is clear from the current work and the presented results by Youssef et al. [20] that the CIVC, indicated by drop in blood flow rate (320 92 ± PU), starts earlier (1.55 21 min), before the drop in the skin temperature. This suggests that the initial ± CIVC is triggered not based on skin temperature threshold, but rather on a certain threshold in the rate of heat dissipation from the skin to the surrounding environment. Under normal temperature (normothermia), the blood vessels are dilated (initial state = vasodilation), with a baseline level of vasoconstrcitive tone [33]. Due to the temperature difference (∆T = Tsk T ) between skin and the − ∞ environment, which is the driving force for heat flow, there is always a certain level of negative heat flux (dissipation) from the skin to the surrounding environment. Once the step-localised cooling is applied, this results in a sudden increase in the temperature difference (∆T = 18 0.6 ◦C in the first . ± two minutes), and consequently, a sudden increase in the heat dissipation rate (Q = 0.15 0.2 W in dis − ± the first two minutes). If this change in the heat dissipation rate is above a certain threshold, the CIVC mechanisms are activated and vasoconstriction prevailed. Then, if the heat dissipation rate reaches a . dQdis constant threshold level ( dt = 0), the vasoconstriction mechanism will be interrupted and revert to vasodilation. Otherwise, the vasoconstriction state is prolonged. It should be stated here that this proposed model leaves a number of questions open for further investigation. One very important question, here, is about the nature of the rate-sensitive receptors and their working mechanism. In their work on the coding of cutaneous temperature and thermal receptors [50], Ran et. al. observed that the responses of cold-responding neurons peaked during the transient cooling phase and rapidly adapted to steady cold stimuli, suggesting that these neurons report temperature changes. In other word, cold-responding neurons report the relative drop in skin dTsk temperature (i.e., rate of temperature change dt ), rather than the absolute value [51]. Additionally, many questions are still open regarding the nature of thermal sensation and thermal-sensory system in relation to thermoregulation [52]. It is possible in our case to use many of the control-system terms to describe autonomic thermoregulation reactions (CIVC/CIVD), such as the regulated (controlled) variable (finger skin temperature), sensors (skin and preoptic area of the hypothalamus), integrator/controller, and effectors or actuators (blood vessels). However, a concept such as the set point in thermoregulation, and in homeostatic regulation in general, has eluded precise identification. Determination of where such a set point is precisely located, how it is consulted, and even more fundamentally, how the precise set-point value is established has been elusive [53]. Therefore, the “balance point” term [54] is suggested to be more suitable in our case, whereby the multiple pathways act independently [55]; integration (or balancing) of the independent pathways, each of which might have different thresholds of activation and inactivation, allows for a relatively well-maintained internal temperature [33,56]. The balance-point framework aids in explaining the physiology while still allowing for a negative feedback approach [53] in describing and reverse engineering the thermoregulatory reactions. Appl. Sci. 2019, 9, x FOR PEER REVIEW 15 of 19

heat dissipation rate reaches a constant threshold level ( = 0), the vasoconstriction mechanism will be interrupted and revert to vasodilation. Otherwise, the vasoconstriction state is prolonged. It should be stated here that this proposed model leaves a number of questions open for further investigation. One very important question, here, is about the nature of the rate-sensitive receptors and their working mechanism. In their work on the coding of cutaneous temperature and thermal receptors [50], Ran et. al. observed that the responses of cold-responding neurons peaked during the transient cooling phase and rapidly adapted to steady cold stimuli, suggesting that these neurons report temperature changes. In other word, cold-responding neurons report the relative drop in skin Appl. Sci. 2019, 9, 3372 16 of 19 temperature (i.e., rate of temperature change ), rather than the absolute value [51].

FigureFigure 13. FlowFlow chart chart explaining explaining the suggested the suggested model of model thermoregulatory of thermoregulatory localised CIVC/CIVD localised CIVCreactions./CIVD reactions. 4. Conclusions Additionally, many questions are still open regarding the nature of thermal sensation and thermal-sensoryThe main goal system of this in relation study was to thermoregulation to gain more physiological [52]. It is possible andmechanistic in our case to insights use many into of thethe underlying control-system processes terms ofto thermoregulatorydescribe autonomic localised thermoregulation CIVC/CIVD reactions reactions (CIVC/CIVD), using a data-based such as mechanisticthe regulated modelling (controlled) (DBM) variable approach. (finger Two skin types temperature), of localised coolingsensors were(skin appliedand preoptic on the area fingers of the of 33hypothalamus), healthy participants integrator/controller, (test subjects), namely, and effectors continuous or actuators and intermittent (blood vessels). cooling, duringHowever, the coursea concept of thesuch conducted as the set experiments. point in thermoregulation, During the first set and of experiments. in homeostatic The resultsregulation showed in general, that 27 participants has eluded outprecise of 33 identification. showed clear evidenceDetermination of the huntingof where reaction such (i.e.,a set cycles point of is CIVC precisely/CIVD located, episodes) how during it is continuousconsulted, localisedand even cooling. more fundamentally, Two different, yethow connected, the precise thermoregulatory set-point value is reactions established representing has been theelusive hunting [53]. reaction, Therefore, namely, the “balance CIVC and point” CIVD term were [5 mathematically4] is suggested modelledto be more and suitable described in our as twocase, separatewhereby processes the multiple or dynamic pathways systems act independently using the DBM [5 approach.5]; integration A second-order (or balancing) discrete-time of the independent transfer functionpathways, (two each poles of which and twomight zeros) have was different the best thresholds (RT = 0.91 of activation0.06 and andYIC inactivation,= 11.43 allows2.65) for for a 2 ± − ± mathematicallyrelatively well-maintained representing theinternal dynamic temperature responses [33,56]. of the fingerThe skinbalance-point temperature framework to step localised aids in cooling and for describing both CIVC and CIVD reactions. For both reactions, it was possible to decompose the obtained second-order system into two first-order TF systems in parallel configurations. The calculated time constants from the two first-order systems suggested two underlying processes for both CIVC and CIVD reactions, one of which is almost 10 times faster. Mechanistic and physiological insights into the suggested underlying processes suggested that the slower (with average τ = 7.36 min) process represents slow convective heat transfer from the capillaries and the conductive heat exchange between the skin and Peltier’s elements. On the other hand, the faster process represents the closing/opening of the AVAs during the CIVC/CIVD reactions, which causes a fast change in the Appl. Sci. 2019, 9, 3372 17 of 19 convective heat transfer from the superficial veins. During the intermittent localised cooling, no test subjects of Exp.2 (in total 12) showed any episodes of CIVD, although the skin temperature reached the same level (16.2 0.7 C) as that under continuous cooling. A new term is suggested in this paper, ± ◦ namely, the latent heat of CIVD (LH-CIVD), which represents the amount of dissipated heat required to trigger the CIVD. It should be stated here that the identified models are limited to the presented methodology of localized cooling. Additionally, in future investigations, interpersonal variations (e.g., physiological and anthropometric variations) should be considered and studied. Moreover, the present work suggested a new model for the thermoregulatory localised CIVC/CIVD reactions. The new model suggested states that, with an initial vasodilation state, the initial localised CIVC is triggered not based on skin temperature threshold, but rather on a certain threshold in the rate of heat dissipation from the skin to the surrounding environment.

Author Contributions: Conceptualisation, A.Y. and J.-M.A.; methodology, A.Y. and A.V.; software, A.Y. and A.V.; validation, A.Y.; formal analysis, A.Y. and A.V.; investigation, A.Y. and A.V.; resources, G.D.B and J-N.A.; data curation, A.Y. and A.V.; writing—original draft preparation, A.Y. and A.V.; writing—review and editing, A.Y. and J.-M.A.; visualisation, A.Y.; supervision, J.-M.A. and A.Y.; project administration, J.-M.A.; funding acquisition, J.-M.A. Funding: This research received no external funding. Conflicts of Interest: The authors declare no conflict of interest.

References

1. Novosel’tsev, V.N. Homeostasis and health: Analysis from a standpoint of the control theory. Autom. Remote Control 2012, 73, 841–851. [CrossRef] 2. Bernard, C. De la Physiologie Générale; Librairie Hachette Et: Paris, France, 1872. 3. Cannon, W.B. The Wisdom of the Body; W.W. Norton: New York, NY, USA, 1939. 4. Ivanov, K.P. The development of the concepts of homeothermy and thermoregulation. J. Therm. Biol. 2006, 31, 24–29. [CrossRef] 5. Ivanov, K. Restoration of vital activity of cooled animals without rewarming the body. Eur. J. Appl. Physiol. 2009, 105, 5–12. [CrossRef][PubMed] 6. Turner, J.S. On the thermal capacity of a ’s egg warmed by a brood patch. Physiol. Zool. 1997, 70, 470–480. [CrossRef][PubMed] 7. Cheung, S.S. Responses of the hands and feet to cold exposure. Temperature 2015, 2, 105–120. [CrossRef] [PubMed] 8. Taylor, N.A.S.; Machado-Moreira, C.A.; van den Heuvel, A.M.J.; Caldwell, J.N. Hands and feet: Physiological insulators, radiators and evaporators. Eur. J. Appl. Physiol. 2014, 114, 2037–2060. [CrossRef][PubMed] 9. Walløe, L. Arterio-venous anastomoses in the human skin and their role in temperature control. Temp. (Austin. Tex.) 2016, 3, 92–103. [CrossRef][PubMed] 10. Grant, R.T.; Bland, E. Observations on arterio venous anastomoses in human skin and in the bird’s foot with special reference to the reaction to cold. 1931, 15, 385–411. 11. Heus, R.; Daanen, H.A.M.; Havenith, G. Physiological criteria for functioning of hands in the cold. Appl. Ergon. 1995, 26, 5–13. [CrossRef] 12. Karaki, W.; Ghaddar, N.; Ghali, K.; Kuklane, K.; Holmér, I.; Vanggaard, L. Human thermal response with improved AVA modeling of the digits. Int. J. Therm. Sci. 2013, 67, 41–52. [CrossRef] 13. Rida, M.; Karaki, W.; Ghaddar, N.; Ghali, K.; Hoballah, J. A new mathematical model to simulate AVA cold-induced vasodilation reaction to local cooling. Int. J. Biometeorol. 2014, 58, 1905–1918. [CrossRef] [PubMed] 14. Lewis, T. Observations upon the reactions of the vessels of the human skin to cold. Heart 1930, 15, 177–208. 15. Daanen, H.A.M. Finger cold-induced vasodilation: A review. Eur. J. Appl. Physiol. 2003, 89, 411–426. [CrossRef][PubMed] 16. Teichner, W.H. Individual Thermal and Behavioral Factors in Cold-Induced Vasodilation. Psychophysiology 1966, 2, 295–304. [CrossRef] Appl. Sci. 2019, 9, 3372 18 of 19

17. Bergersen, T.K.; Hisdal, J.; Walløe, L. Perfusion of the human finger during cold-induced vasodilatation. Am. J. Physiol. 1999, 276, R731–R737. [CrossRef][PubMed] 18. Lee, J.Y.; Bakri, I.; Matsuo, A.; Tochihara, Y. Cold-induced vasodilation and vasoconstriction in the finger of tropical and temperate indigenes. J. Therm. Biol. 2013, 38, 70–78. [CrossRef] 19. Cheung, S.S.; Daanen, H.A.M. Dynamic Adaptation of the Peripheral Circulation to Cold Exposure. 2012, 19, 65–77. [CrossRef] 20. Youssef, A.; D’Haene, M.; Vleugels, J.; de Bruyne, G.; Aerts, J.-M. Localised Model-Based Active Controlling of Blood Flow During Chemotherapy to Prevent Nail Toxicity and Onycholysis. J. Med. Biol. Eng. 2018, 39, 139–150. [CrossRef] 21. Bladt, L.; De Clercq, J.; Janssens, T.; Van Hulle, J.; Vleugels, J.; Aerts, J.M.; De Bruyne, G. Cold-induced vasoconstriction for preventing onycholysis during cancer treatment. Extrem. Physiol. Med. 2015, 4, A60. [CrossRef] 22. Steckel, J.; Goethijn, F.; de Bruyne, G. A research platform using active local cooling directed at minimizing the blood flow in human fingers. In Proceedings of the 7th International Conference on Pervasive Computing Technologies for Healthcare and Workshops, Venice, Italy, 5–8 May 2013; pp. 81–84. 23. Aerts, J.M.; Berckmans, D.; Saevels, P.; Decuypere, E.; Buyse, J. Modelling the static and dynamic responses of total heat production of broiler chickens to step changes in air temperature and light intensity. Br. Poult. Sci. 2000, 41, 651–659. [CrossRef] 24. Young, P.C. Control and Dynamic Systems: Advances in Theory and Applications; Leondes, C.T., Ed.; New Academic Press Inc Elsevier Science: New York, NY, USA, 1989. 25. Young, P.C. Data-based mechanistic modelling of environmental, ecological, economic and engineering systems. Environ. Model. Softw. 1998, 13, 105–122. [CrossRef] 26. Youssef, A.; Dekock, J.; Ozcan, S.E.; Berckmans, D. Data-Based Approach to Model the Dynamic Behaviour of Greenhouse Temperature. Acta Hortic. 2011, 893, 931–938. [CrossRef] 27. Youssef, A.; Exadaktylos, V.; Berckmans, D. Modelling and quantification of the thermoregulatory responses of the developing avian embryo: Electrical analogies of a physiological system. J. Therm. Biol. 2014, 44, 14–19. [CrossRef][PubMed] 28. Youssef, A.; Exadaktylos, V.; Ozcan, S.E.; Berckmans, D. Proportional-Integral-Plus (PIP) Control System for Individual Thermal Zones in a Small Ventilated Space. ASHRAE Trans. 2011, 117, 48–56. 29. Youssef, A.; Yen, H.; Özcan, S.E.; Berckmans, D. Data-based mechanistic modelling of indoor temperature distributions based on energy input. Energy Build. 2011, 43, 2965–2972. [CrossRef] 30. Young, P.C.; Jakeman, A. Refined instrumental variable methods of recursive time-series analysis Part III. Extensions. Int. J. Control 1980, 31, 741–764. [CrossRef] 31. Young, P.C. Recursive Estimation and Time-Series Analysis: An Introduction for the Student and Practitioner; Springer: Heidelberg, Berlin, 2011. 32. Young, P.C.; Chotai, A.; Tych, W. Identification, Estimation and Control of Continuous-Time Systems Described by Delta Operator Models; Kluwer Academic Publishers: Dordrecht, the Netherlands, 1991. 33. Tansey, E.A.; Johnson, C.D. Recent advances in thermoregulation. Adv. Physiol. Educ. 2015, 39, 139–148. [CrossRef] 34. Lienhard, J.H. A Heat Transfer Textbook; Phlogiston Press: Cambridge, MA, USA, 2001. 35. Yamazaki, F.; Sone, R.; Zhao, K.; Alvarez, G.E.; Kosiba, W.A.; Johnson, J.M. Rate dependency and role of in the vascular response to direct cooling in human skin. J. Appl. Physiol. 2006, 100, 42–50. [CrossRef] 36. Johnson, J.M.; Yen, T.C.; Zhao, K.; Kosiba, W.A. Sympathetic, sensory, and nonneuronal contributions to the cutaneous vasoconstrictor response to local cooling. Am. J. Physiol. Circ. Physiol. 2005, 288, H1573–H1579. [CrossRef] 37. Nuzzaci, G.; Evangelisti, A.; Righi, D.; Giannico, G.; Nuzzaci, I. Is There Any Relationship between Cold-Induced Vasodilatation and Vasomotion? Microvasc. Res. 1999, 57, 1–7. [CrossRef] 38. Sheppard, L.W.; Vuksanovi´c,V.; McClintock, P.V.E.; Stefanovska, A. Oscillatory dynamics of vasoconstriction and vasodilation identified by time-localized phase coherence. Phys. Med. Biol. 2011, 56, 3583–3601. [CrossRef][PubMed] 39. Kellogg, D.L. In vivo mechanisms of cutaneous vasodilation and vasoconstriction in humans during thermoregulatory challenges. J. Appl. Physiol. 2006, 100, 1709–1718. [CrossRef][PubMed] Appl. Sci. 2019, 9, 3372 19 of 19

40. Johnson, J.M.; Minson, C.T.; Kellogg, D.L. Cutaneous vasodilator and vasoconstrictor mechanisms in temperature regulation. Compr. Physiol. 2014, 4, 33–89. [PubMed] 41. Castellani, J.W.; O’Brien, C. Peripheral Vasodilation Responses to Prevent Local Cold Injuries. In Prevention of Cold Injuries; RTO: Neuilly-sur-Seine, France, 2005; pp. KN2-1–K2-14. 42. Pérgola, P.E.; Kellogg, D.L.; Johnson, J.M.; Kosiba, W.A.; Solomon, D.E. Role of sympathetic nerves in the vascular effects of local temperature in human forearm skin. Am. J. Physiol. 1993, 265, H785–H792. [CrossRef] [PubMed] 43. Sendowski, I.; Sarourey, G.; Besnard, Y.; Bittel, J. Cold induced vasodilatation and cardiovascular responses in humans during cold water immersion of various upper limb areas. Eur. J. Appl. Physiol. Occup. Physiol. 1997, 75, 471–477. [CrossRef] 44. Keramidas, M.E.; Musizza, B.; Kounalakis, S.N.; Mekjavic, I.B. Enhancement of the finger cold-induced vasodilation response with exercise training. Eur. J. Appl. Physiol. 2010, 109, 133–140. [CrossRef] 45. Flouris, A.D.; Westwood, D.A.; Mekjavic, I.B.; Cheung, S.S. Effect of body temperature on cold induced vasodilation. Eur. J. Appl. Physiol. 2008, 104, 491–499. [CrossRef] 46. Flouris, A.D.; Cheung, S.S. Thermal Basis of Finger Blood Flow Adaptations During Abrupt Perturbations in Thermal Homeostasis. Microcirculation 2011, 18, 56–62. [CrossRef] 47. Flouris, A.D.; Cheung, S.S. Influence of thermal balance on cold-induced vasodilation. J. Appl. Physiol. 2009, 106, 1264–1271. [CrossRef] 48. Daanen, H.A.; Ducharme, M.B. Finger cold-induced vasodilation during mild , and at thermoneutrality. Aviat. Space Environ. Med. 1999, 70, 1206–1210. 49. Mekjavic, I.B.; Dobnikar, U.; Kounalakis, S.N.; Musizza, B.; Cheung, S.S. The trainability and contralateral response of cold-induced vasodilatation in the fingers following repeated cold exposure. Eur. J. Appl. Physiol. 2008, 104, 193–199. [CrossRef][PubMed] 50. Ran, C.; Hoon, M.A.; Chen, X. The coding of cutaneous temperature in the spinal cord. Nat. Neurosci. 2016, 19, 1201–1209. [CrossRef][PubMed] 51. Vandewauw, I.; Voets, T. Heat is absolute, cold is relative. Nat. Neurosci. 2016, 19, 1188–1189. [CrossRef] [PubMed] 52. Kobayashi, S. Temperature receptors in cutaneous nerve endings are thermostat molecules that induce thermoregulatory behaviors against thermal load. Temp. (Austin. Tex.) 2015, 2, 346–351. [CrossRef][PubMed] 53. Tan, C.L.; Cooke, E.K.; Leib, D.E.; Lin, Y.C.; Daly, G.E.; Zimmerman, C.A.; Knight, Z.A. Warm-Sensitive Neurons that Control Body Temperature. Cell 2016, 167, 47–59. [CrossRef][PubMed] 54. Romanovsky, A.A. Thermoregulation: Some concepts have changed. Functional architecture of the thermoregulatory system. Am. J. Physiol. Integr. Comp. Physiol. 2007, 292, R37–R46. [CrossRef] 55. McAllen, R.M.; Tanaka, M.; Ootsuka, Y.; McKinley, M.J. Multiple thermoregulatory effectors with independent central controls. Eur. J. Appl. Physiol. 2010, 109, 27–33. [CrossRef][PubMed] 56. Fealey, R.D. Interoception and reflexes thermoregulation. Handb. Clin. Neurol. 2013, 117, 79–88.

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