Proceedings: Building Simulation 2007

THERMAL MODEL OF BODY REGULATION CONSIDERING INDIVIDUAL DIFFERENCE

Satoru Takada1, Hiroaki Kobayashi2, and Takayuki Matsushita1

1Department of Architecture, Graduate School of Engineering, Kobe University, Rokko, Nada, Kobe 657-8501, Japan 2Department of Architecture and Civil Engineering, Graduate School of Science and Technology, Kobe University Rokko, Nada, Kobe 657-8501, Japan

state. However, the difference in body temperature ABSTRACT regulation between real subjects makes it difficult; This paper proposes the methodology to quantify the Even for one environmental condition, more than one individual difference in temperature regulation of kinds of experimental results are obtained from for transient simulation of body several subjects, while a model gives one result for temperature. one condition. In other words, the problem of individual difference cannot be avoided for the Experiments of transient thermal exposure were validation of thermal model of human body. conducted for four subjects and the characteristics of individual difference in themoregulatory response Havenith (2001) proposes to express individual were observed quantitatively. As the result, the differences in the human model by differences in core temperature and rate were giving several individual characteristics such as body significant. surface area, mass and body fat into the model. In that work, the simulated results with consideration of For each subject, the physiological coefficients used individual difference are compared with those in the two-node model were adjusted in order to without consideration, but the improvement by the minimize the difference between experimental and consideration is not so clear. Zhang et al. (2001) uses calculated values in a series of a representative ‘body builder model’ that expresses the individual transient state in core and . With the difference by inputting similar elements as Havenith. combination of the coefficients determined, the skin However the simulated results are shown only for a and core calculated with the two-node steady state and not checked from the viewpoint of model agreed well with the experimental results for transient state. all the subjects involved in the experiments. This shows that the individual difference in the regulation Individual difference in thermoregulation in human of body temperature is well described with the body is often mentioned, but the element that causes combination of the coefficients determined by the the difference is not clarified and the several optimization. elements would be related to each other. Moreover, not only static but also dynamic response of human KEYWORDS body is related to the data. From that viewpoint, this paper presents a methodology of expressing the Temperature regulation model, Two-node model, individual difference in dynamic thermoregulation of Individual difference, Subject experiment, human body using human thermal model (two-node Optimization model). In the first part of the paper, the individual difference in thermoregulation of human body is INTRODUCTION shown quantitatively by experiments involving four Thermal model of human body plays important role subjects (naked, sedentary). In the latter part, based in the design of comfortable architectural on the experimental data of core and skin environment. The two-node model is widely used in temperatures, the physiological constants (set point a lot of situations such as calculation of SET*, and temperature of core and skin, coefficients in the there are a lot of models proposed and simulated dynamic model of regulatory sweating and skin results shown (Gagge et al. 1986, ASHRAE 2005). blood flow) included in two-node model (Gagge et al. Recently, not only for steady state but also for 1971) are optimized so that the difference between transient state, the results of simulations are the experimental and the calculated values should presented, but the validity of the model in transient become smallest as a whole transient process. It is state is not clarified enough so far. In order to show shown that by using the determined coefficients, a the validity, the calculated results should be subject experiment under another kind of thermal compared with the experimental results in transient transients can be predicted and that the combination

- 725 - Proceedings: Building Simulation 2007 of the coefficients describes the characteristics of the Table 2 Measured items and methods individual difference. ITEM METHOD (INSTRUMENT) SUBJECT EXPERIMENT Core temperature Thermocouple (T type, 0.2 mm (tympanic, rectal) in diameter) Method Skin temperature Thermocouple (T type, 0.2 mm Four healthy students seated back-to-back are (head, forearm, back in diameter) exposed to a thermal transient, which starts with of hand, instep, calf, thermally neutral condition followed by a low air thigh, abdomen) temperature, the second neutral condition, a high air Heart rate Photoelectric pulse wave temperature, and at last the third neutral condition method (Cat Eye) (Figure 1). All the subjects wear trunks only and Body weight Electric balance (Mettler keep sedentary one hour before the experiment starts Toledo KCC 150) in the thermally neutral condition (29 deg. C, 50%rh). Air and globe Thermocouple (T type, 0.2mm temperatures in diameter) During experiments, core temperatures and skin Relative humidity Electric resistance method (T temperatures, heart rate and the environmental and D, TR-72S) conditions (air temperature, humidity, globe Wind velocity Hot wire method (Kanomax, temperature, wind velocity) are measured 6543), continuously with the interval of 10 seconds. For skin temperature, Hardy and DuBois seven points are Result measured. The measured items are shown in detail in As shown in Figure 2, the difference in rectal Table 2. temperature between subjects reaches 1 [K] at Table 1 Information on subjects maximum. This is a significant difference from the viewpoint of numerical model of thermoregulation of AGE HT WT SEX BSA human body, because 1 [K] difference in core 2 [year] [cm] [kg] [-] [m ] temperature brings a significant difference in A 25 169 55.6 Male 1.64 thermoregulatory responses such as skin blood flow B 24 167 66.0 Male 1.73 rate and sweat rate. As for the tendency in change, C 24 163 54.8 Male 1.59 difference between subjects is significant. For D 24 174 76.8 Male 1.89 example, during the process in the low temperature HT: Height, WT: Weight, BSA: Body surface area room (condition of 20 deg. C in air temperature), the calculated from height and weight (Kurazumi 1994) rectal temperature of Subject D rises while that of Subject B decreases. The time when the rectal Room A Room A Room BRoom A Room B Room A 29℃ 29℃ 20℃29℃ 38℃ 29℃ ● ● ●● ●●● temperature reaches a maximum or minimum and the -60P re p aration 0 30 50 80 100 120 [m in] range of variation are different from subject to Relative humidity: 50%, C lothing: Trunks only, S e a te d subject. Figure 1 Schedule of experiment As shown in Figure 3, the individual difference is seen similarly for the tympanic temperature. In Figure 4, the averaged skin temperature (Hardy and DuBois seven points) is shown. The difference between subjects reaches 1 [K]. By nature the range of variation is wider than core temperature. Therefore it can be said that the individual difference in skin temperature is smaller than that in core temperature. The heart rate is shown in Figure 5. The difference is significant and this suggests the individual difference in the characteristics in the regulation of the blood flow. Table 3 shows the body weight loss during experiment. The loss of subject B and D is more than the others and this suggests the difference in quantity of sweat perspired during the experiment and also the difference in regulatory sweating response. As shown in Table 4, the room air temperature and humidity were controlled slightly different from the setting shown in Figure 1, and the movement of

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subjects between rooms was started at the scheduled 120 C time and it was necessary to take c.a. 1 minute to go B 100 out the former room. 80

Table 3 Weight loss (difference between before and 60 after experiment)

40 Heart rate[1/min] Heart AD WEIGHT LOSS 20 [g/h] [g/(h･m2)] (per body surface area) 29℃ 20℃ 29℃ 38℃ 29℃ 0 A 61.4 37.0 0 102030405060708090100110120 B 89.9 52.9 Time[min] C 53.8 33.6 Figure 5 Heart rate (Experiment) D 94.5 52.0

Table 4 Environmental conditions (Measured values 38 B averaged for time) D C 37.5 Time[min] 0 to 31 31 to 51 51 to 81 81 to 101 101 to 120 Room A Room B Room A Room B Room A Air te m p e ratu re [℃ ] 2 9 .4 20.029.4 40.9 29.4 37 Relative humidity[% ] 4 7 .5 55.647.6 53.5 47.8 Globe tem perature[℃] 29.6 20.229.5 40.2 29.6 36.5 Wind velocity [m / s] 0 .10 0.24 0.10 0.12 0.12 A 36 ANALYSIS USING TWO-NODE MODEL Rectal Rectal temperature[℃] 35.5 29℃ 20℃ 29℃ 38℃ 29℃ Method 35 0 102030405060708090100110120 In the two-node model (Gagge 1971), the Time[min] thermoregulatory responses are expressed as Figure 2 Rectal temperature (Experiment) following equations. For sweating rate, 1 1 38 m = pr3 ⋅ ()()T − pr1 T − pr 2 ⋅ ⋅ sw cr sk 3600 1000 37.5 (1) 37 C , if the value of a bracket is minus, the value of the 36.5 bracket should be displaced as zero.

36 A D For skin blood flow rate, B Tympanic temperature[℃] Tympanic 35.5 pr4 + pr5(T − pr1) 1 29℃ 20℃ 29℃ 38℃ 29℃ cr (2) vbl = ⋅ 35 1+ pr6()pr2 −Tsk 3600 0 102030405060708090100110120 Time[min] , if the value of a bracket is minus, the value of the bracket should be displaced as zero. Figure 3 Tympanic temperature (Experiment) In these equations, there are six coefficients included and the values of them are given in the original paper. 37 Some of the coefficients were determined based on thermophysiological experiment, and for the others, 36 A 35 D the process of determination is not clear. The model would be tuned to measured results of a specific 34 subject. Anyway, the individual difference is not 33 taken into account in the two-node model. Thus in 32 C this paper, the six coefficients are adjusted for each 31 B subject.

Averaged skin temperature[℃] skin Averaged 30 29℃ 20℃ 29℃ 38℃ 29℃ The six coefficients included in the two-node model 29 0 102030405060708090100110120 are determined so that the difference between Time[min] calculated and experimental core and skin temperatures becomes smallest. Figure 4 Averaged skin temperature (Experiment) For six coefficients, candidates of the solution are prepared among the assumed domain as shown in

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Table 5. The number of the combination is 1,260,000. al., the original authors) are compared in Figures 6 to The objective function is shown in equation (3). 9 for both core and skin temperatures, for each

N N subject. For all the subjects, the calculated results ′ 2 ′ 2 (3) with determined coefficients agreed with the J = ∑{}{}(Tcr,i − Tcr,i ) + ∑ (Tsk ,i − Tsk ,i ) i=1 i=1 experimental results better than those with default As the experimental data, the mean skin temperature coefficients. This means that the parameters were (Hardy and DuBois seven points) and rectal tuned well to describe the experimental values of temperature are used for skin and core temperatures each subject. respectively. The interval of data acquisition was 10 Table 7 Combination of parameters minimizing seconds. Therefore the total number of the time difference between experimental and calculated skin series data is 721 for two hours experiment. and core temperatures in two-node model for each The experimental values are given for the initial subject condition of skin and core temperature in the P aram e te r P r1 P r2 P r3 P r4 P r5 P r6 calculation. For the boundary condition, the raw data Subject Basal b lood T T Perspiration Vaso dilation Vaso of the room air temperature and humidity are cr,set sk,set flow rate constriction [g/ (m 2・h・K 2)] [kg/(m 2・h・K)] inputted to the calculation program. As the mean [℃ ] [℃ ] [kg/(m 2・h)] [1/K] radiant temperature, the air temperature was given, A 36.1 32.7101.26 15 0.00625 B 36.9 32.3200.07875 15 0.00625 because the difference between the globe C 36.7 32.1202.52 30 0.00625 temperature and the air temperature was small D 37.1 33.1 100 7.56 7.50.00625 default 36.6 34.1 100 6.3750.5 enough as shown in Table 4.

The detailed conditions of calculation are shown in 38 Table 6. The mass and the surface area of the subject core cal.(optimized) cal.(default) are as shown in Table 1. The mass ratio of core and 37 36 skin was set to 95 :5 (Gagge et al. 1971). exp. 35 cal.(optimized) Table 5 Candidates of parameters in the two-node 34 skin mode in optimization (All the combinations for these 33 exp. six parameters are tried in the calculations.) 32 Temperature[℃] pr1pr2pr3pr4pr5pr6 31 cal.(default) 37.734.7 100 12.61501 30 37.534.5 80 10.08 120 0.8 29℃ 20℃ 29℃ 38℃ 29℃ 37.334.3607.56 90 0.6 29 37.134.1405.04 60 0.4 0 102030405060708090100110120 Time[min] 36.933.9202.52 30 0.2 36.733.7101.26 15 0.1 36.533.550.63 7.50.05 Figure 6 Calculated and measured results for 36.333.30.315 3.75 0.025 Subject A (Core and skin temperatures) 36.133.10.1575 0.0125 35.932.90.07875 0.00625 35.732.7 35.532.5 39 35.332.3 core exp. cal.(optimized) 35.132.1 38 34.931.9 37 36 cal.(default) cal.(default) Table 6 Calculation conditions 35 exp. Air te m p e ra tu re M e a su re d d a ta 34 33 skin Air humidity M easured data cal.(optimized) Temperature[℃] 32 MRT Equal to a ir te m p e ra tu re 31 C onvectiv e h e a t tra n sfe r 30 3.1[W /(m 2･K )] 29℃ 20℃ 29℃ 38℃ 29℃ coefficient 29 0 102030405060708090100110120 Radiativ e h e a t tra n sfe r 2 4.65[W /(m ･K )] Time[min] coefficient Clothing 0.1[clo] Figure 7 Calculated and measured results for Metabolic ra te 2 58.2[W/m ] Subject B (Core and skin temperatures) E xte rn a l mechanical 0 e fficiency Result The coefficients determined are shown in Table 7. The experimental results, the calculated results with the determined coefficients and the calculated results with the default coefficients (proposed by Gagge et

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38 core exp. cal.(optimized) Table 8 Environmental conditions (Measured values 37 averaged for time) 36 cal.(default) Time[min] 0 to 3 2 3 2 to 6 1 6 1 to 1 2 0 Room A Room B Room A 35 cal.(default) Air tem perature[℃] 29.435.226.3 cal.(optimized) 34 Relative humidity[%] 47.147.346.0 Globe tem perature[℃] 29.635.027.0 33 Wind velocity [m / s] 0 .10 0.11 0.12 skin exp. 32 Temperature[℃] 31 30 29℃ 20℃ 29℃ 38℃ 29℃ The results are shown in Figures 11 to 14. For all the 29 subjects, the calculated results agree well with the 0 102030405060708090100110120 Time[min] experimental results. By using the combination of coefficients optimized from a series of thermal Figure 8 Calculated and measured results for transients experiment, the experimental results of Subject C (Core and skin temperatures) another series of thermal transients were explained well. This indicates that the determined coefficients 38 cal.(optimized) core exp. in the two-node model describe well the body 37 cal.(default) temperature regulation system of the each subject. 36 cal.(default) 35 38 core cal.(optimized) exp. 34 cal.(optimized) 37 33 exp. skin cal.(default) 32 36 Temperature[℃] 31 cal.(default) 35 30 29℃ 20℃ 29℃ 38℃ 29℃ 29 34 Temperature[℃] skin 0 102030405060708090100110120 cal.(optimized) exp. Time[min] 33 29℃ 35℃ 26℃ Figure 9 Calculated and measured results for 32 Subject D (Core and skin temperatures) 0 102030405060708090100110120 Time[min] DISCUSSION Figure 11 Calculated and measured results for Subject A (Core and skin temperatures) It was shown that by selecting properly the six cal.(optimized) coefficients related to body temperature regulation in 38 core the two-node model, the solution of two-node model agrees well with the experimental results. 37 cal.(default) 36 exp. In order to ensure that the determined coefficients cal.(default) describe the characteristics of the body temperature 35 regulation of each subject well, a test is done in this exp. 34 Temperature[℃] section. The problem is whether the calculated skin cal.(optimized) results by the two-node model with the determined 33 coefficients agree with experimental results under 29℃ 35℃ 26℃ 32 another series of thermal transients or not. 0 102030405060708090100110120 Time[min] Another type of experiment was conducted at the same time, at the same week as the first experiment, Figure 12 Calculated and measured results for for the same four subjects, and in the same manner. Subject B (Core and skin temperatures) Only the room air temperature condition is different cal.(optimized) exp. as shown in Figure 10. 38 core The environmental conditions measured in the 37 cal.(default) experiment are shown in Table 8 as averaged values 36 for each process. Like as the first experiment, they cal.(default) 35 are slightly different from the setting and the exp. 34

measured values are inputted to the calculations. Temperature[℃] skin cal.(optimized) Room A Room A R o o m B R o o m A 29℃ 29℃ 35℃ 26℃ 33 ●●●●● 29℃ 35℃ 26℃ -60Preparation 0 30 60 120 [m in] 32 Relative humidity: 50%, C lothing: Trunks only, M e ta b o lism : Seated 0 102030405060708090100110120 Time[min] Figure 10 Schedule of experiment for verification

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Figure 13 Calculated and measured results for transient case of subject experiments for the same Subject C (Core and skin temperatures) member of subjects were simulated, and the

exp. calculated results, again showed good agreement 38 core with the experimental results. Therefore it was 37 shown that the combination of the parameters cal.(optimized) cal.(default) determined in this paper describe the characteristics 36 cal.(default) in dynamic thermoregulatory responses of each 35 subject. cal.(optimized) 34 Temperature[℃] skin ACKNOWLEDGEMENTS exp. 33 29℃ 35℃ 26℃ Subject experiments in this research were conducted 32 at the Techno-amenity Laboratory of Katsura-Int'tech 0 102030405060708090100110120 Time[min] Center, Graduate School of Engineering, Kyoto University. Figure 14 Calculated and measured results for This research was partially supported by the Ministry Subject D (Core and skin temperatures) of Education, Science, Sports and Culture, Grant-in- In the two-node model (Gagge et al. 1971) used in Aid for Young Scientists (A), 17686050, 2005. this study, the model of shivering is not included. From 30 min to 50 min in the first experiment shown NOMENCLATURE in Figure 1, the air temperature is 20 deg. C and m : Regulatory sweating rate [kg/(m2･s)] shivering was observed for a part of subjects. In the sw 2 newer version of two-node model (Gagge et al. vbl: Skin blood flow rate [kg/(m ･s)] 1986), a shivering model is included. By adding the shivering model to this calculation, the determined pr1: set point of core temperature [deg. C] coefficients did not change significantly. pr2: set point of skin temperature [deg. C] In this paper, as the definition of the objective pr3: Coefficient of sweating rate model [g/(m2･h･ function, the rectal and the mean skin temperatures K2)] are summed up with an equal weight, 1:1 as shown in equation (3). However another way of weighting is pr4: Skin blood flow rate in thermally neutral possible, and there are other methods using other condition [kg/(m2・ h)] data like blood flow rate, sweating rate, or a skin pr5: Coeffcients of vasodilation [kg/(m2・ h・ K)] temperature measured at some part of the body (not averaged) as an element of the objective function to pr6: Coefficients of vasoconstriction [1/K]. optimize the parameters. Tcr: Calculated core temperature [deg. C]

CONCLUSION Tsk: Calculated skin temperature [deg. C] ’ Experiments of transient thermal exposure were Tcr : Measured rectal temperature [deg. C] conducted for four subjects and the characteristics of ’ individual difference in themoregulatory response Tsk : Measured skin temperature (averaged) [deg. C] were observed quantitatively. As the result, the N：Number of data obtained in a series of transient differences in core temperature and heart rate were state (In the experiment in this paper, the data were significant. collected for 120 minutes with the interval of 10 At the same time, a methodology of quantitative seconds, and therefore N=721.) description of individual difference in thermoregulatory responses of human body was REFERENCES proposed considering transient state. The thermoregulatory parameters included in the two- ASHRAE. 2005. “Handbook Fundamentals” Chapter node model were tuned in order to minimize the 8. difference between experimental and calculated results during a transient condition including Fanger P.O. 1970. . Copenhagen: stepwise air temperature change of coming and going Danish Technical Press to lower and higher temperature condition from Gagge A.P. Stolwijk J.A.J. Nishi Y. 1971, “An thermally neutral condition. With the use of the effective temperature scale based on a simple determined combination of parameters, the calculated model of human physiological regulatory results agreed well with the experimental results both response.” ASHRAE Transactions. 77: 247-262. for skin and core temperatures for all four subjects. In order to verify the determined parameters, another Gagge A.P. Fobelets A.P. Berglund L.G. 1986, “A standard predictive index of human response to

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the thermal environment” ASHRAE S：body surface area[m2] Transactions, 92: 709-731. T：temperature[deg. C] Havenith G. 2001. “Individualized model of human t：time [s] thermoregulation for the simulation of heat stress response.” J. Applied Physiology. 90: η：working efficiency [n.d.] 1943-1954. M：Metabolic rate [W/m2] Kurazumi Y. Horikoshi T. Tsuchikawa T. Matsubara q ：Heat loss by respiration [W/m2] N. 1994. “The body surface area of Japanese.” res Japanese J. Biometeorology. 31(1): 5-29. Kmin：Minimum heat conductance by skin tissue [W/(m2･K)]． Zhang H. Huizenga C. Arens E. Yu T. 2001. “Considering individual physiological α：Heat transfer coefficient [W/(m2･K)] differences in a human thermal model.” J. F ：Heat transfer efficiency of clothing [n.d.] Thermal Biology. 26: 401-408. cl 2 qdiff：Heat loss by skin diffusion [W/m ] APPENDIX 2 qrsw：Heat loss by regulatory sweating [W/m ] Basic equations of the two-node model (Gagge et al. φ ： 1971) used in this paper are shown here. a Relative humidity [n.d.] ： The heat balance equation for core node Pa Saturated vapor pressure of ambient air [mmHg] r：evaporative heat of water [J/kg] ccrWcr dTcr = (1−η)M − qres − (cbl vbl + K min ) ⋅ (Tcr − Tsk ) 2 S dt qmax：Maximum heat loss by evaporation [W/m ]

(A1) Psk：Saturated vapor pressure due to skin temperature [mmHg] The heat balance equation for skin node α’：Moisture transfer coefficient [kg/(m2･s･mmHg)] cskWsk dTsk = (Tcr − Tsk ) ⋅ (Kmin + cblvbl ) S dt Fpcl：Vapor transfer efficiency of clothing [n.d.]

− (αc + αr ) ⋅ (Tsk − To ) ⋅ Fcl − (qdiff + qrsw ) prsw：Skin wetness due to regulatory sweating [n.d.] (A2) pwet：Skin wetness [n.d.] The elements appearing in equations (A1) and (A2) clo：Thermal resistance of clothing [clo] are described as follows.

The heat loss by respiration SUFFIX q = 0.0023× M ()44 −φ P (A3) res a a cr：core The heat loss by sweating sk：skin Tsk −Tsk , set 3.0 qrsw = r ⋅ msw ⋅ 2.0 (A4) bl：blood The heat loss by skin diffusion c：convective r：radiative qdiff = pwet ⋅ qmax − qrsw (A5) where, o：ambient set: set point qmax = r ⋅α′⋅(Psk −φa ⋅ Pa )⋅ Fpcl (A6) The values not defined in this paper are same as p = q q (A7) rsw rsw max those in the original paper (Gagge et al. 1971) pwet = 0.06 + 0.94⋅ prsw (A8) 1 Fcl = (A9) 1+ 0.155 ⋅ (α c + α r ) ⋅ clo

NOMENCLATURE c：specific heat [J/(kg･K)] W：mass[kg]

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