1- Thermal response of cutaneous thermoreceptors: A new criterion for the human body thermal sensation

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1 University of Birjand From the SeletedWorks of Dr Alireza Zolfaghari November, - Thermal response of utaneous thermoreeptors: A ne riterion for the human body thermal sensation Alireza Zolfaghari Mehdi Maerefat Available at:

2 Proeedings of the 7th Iranian Conferene of Biomedial Engineering (ICBME, - November Thermal response of utaneous thermoreeptors: A ne riterion for the human body thermal sensation Alireza Zolfaghari Department of Mehanial Engineering Tarbiat Modares University Tehran, Iran a.zolfaghari@modares.a.ir Mehdi Maerefat Department of Mehanial Engineering Tarbiat Modares University Tehran, Iran maerefat@modares.a.ir Abstrat So far, all of the thermal sensation models have been developed on the basis of energy balane equations for eah ompartment of the human body. But, the human body feels thermal environment by response of utaneous thermoreeptors, not by balane of energy. Therefore, the mentioned models are not in onformity ith the physiology of thermal sensation and beause of this, they an not aurately predit the thermal sensation of the human body in some omplex onditions. For the mentioned reasons, e attempt to represent the human body thermal sensation as a funtion of the thermoreeptors response. Aordingly, in the present study, a ne riterion index for evaluating the thermal sensation has been introdued on the basis of utaneous thermal responses. This index has been verified by extensive omparisons ith the published analytial and experimental results here a good agreement as found under both steady-state and transient onditions. Therefore, the ne riterion index an be utilized for evaluating of the body thermal sensation in a ide range of personal/environmental onditions. Keyords- thermal response; thermal sensation; utaneous thermoreeptors I. INTRODUCTION In the past four deades, several mathematial thermal sensation models have been extensively developed due to the neessity in many appliations suh as designing HVAC systems, in the ar industry and in aerospae, mediine, and military appliations. All of these models are based on the energy balane equations for the human body. But, it should be noted that the human thermal sensation is not physially related to the energy balane of the human body. In other ords, the thermal sensation has a diret relationship ith thermal response of skin thermoreeptors, not ith energy balane of the body []. Skin plays a variety of important roles inluding sensory, thermoregulatory and host defense. As shon in Fig., skin tissue is subdivided into three layers: epidermis, dermis and sub-utaneous tissue. Physiologially, the sensory nerve endings and the thermoreeptors distribute in the middle of the epidermis []. The thermoreeptors are the sensors that signal the onditions of the environment to the brain as thermal pereption []. Warm sensation an be eliited only from arm-reeptors and similarly, old sensation an be felt only by old-reeptors. It should be noted that a ide range of thermal response models have been developed for estimating the impulse rate of utaneous thermoreeptors. But, these models have not been used for evaluating the thermal sensation of the human body until no. In 99, Ring and de Dear [] developed a ne human thermal response model on the basis of Hensel [5] findings about the transient response of utaneous thermoreeptors. In spite of its straightforard advantages suh as simpliity and auray, the model of Ring and de Dear [] as not utilized in thermal sensation studies. The main reason for this limitation is that the mentioned model represents the human thermal response in Hz and it does not onform to the standard sale [6] of thermal sensation. It seems that an effetive solution of this problem is to express the thermal response index in the standard sale of thermal sensation. In the present study, e try to find a relation beteen the thermal response index (R and ASHRAE standard thermal sensation index (. Subsequently, e ill present a ne riterion index to express the human thermal sensation as a funtion of the utaneous thermoreeptors responses. II. RESPONSE OF CUTANEOUS THERMORECEPTORS In 99, Ring and de Dear [] developed a simple model of thermoreeptor impulse frequeny. This model assumed the thermo-reeptor response as to parts: a stati part and a dynami part. The stati part of the thermoreeptor response depends upon temperature of thermoreeptors and the dynami part of the thermoreeptor response is proportionally related to temperature hange rates at the depth of the thermoreeptors, dt/dt, ith positive oeffiients for arm reeptors and negative oeffiients for old reeptors [, 7-9]. Aordingly, they desribed the response of the old and arm reeptors, respetively, as follos: T( R ( = ( T( n Kd min., ( t R T( R ( = + ( T( n + Kd max., ( t R //$6. IEEE

3 Figure. Cross-setional vie of the skin. here R( is the response of a thermoreeptors (Hz and K s and K d are the proportionality onstants for the stati and dynami responses. Also, x is the thermoreeptor depth belo the surfae (.5 mm for arm reeptors and. mm for old reeptors. Also, it should be noted that the time-dependent temperature at the depth of the thermoreeptors an be alulated by the STB model []. Zolfaghari and Maerefat [] have shon that the STB model is able to aurately predit the temperature and its hange rate in the utaneous layer under a ide range of personal/environmental onditions. III. A NEW CRITERION FOR THERMAL SENSATION A. Aims and objetives As mentioned previously, although the model of Ring and de Dear [] has several advantages, it is not utilized for evaluating thermal sensation of the human body yet. To remedy this defiieny, it seems that the thermal response index (R must be expressed in the ASHRAE thermal sensation sale. Therefore, in the present study, e attempt to represent the human body thermal sensation as a funtion of the thermoreeptors response. Subsequently, e ill present a ne riterion index to express the human thermal response in the ASHRAE standard thermal sensation sale. B. ASHRAE thermal sensation ASHRAE [6] suggests the as a standard index for evaluating the human thermal sensation. The definition of is based on Gagge s to-node model. This index an be alulated as follos C. Defining a ne index As expressed in Eq. (, the thermal sensation index ( is a funtion of the body temperature (T b. In addition, it is obvious that the body temperature must be related to the thermoreeptors temperature. Therefore, a relationship ould be found beteen the thermal sensation and the temperature of thermoreeptors. On the other hand, Eqs.( and ( indiate that the thermal response index (R is a linear funtion of the thermoreeptors temperature under steady-state onditions. Therefore, the an be ritten as a funtion of thermal response under steady-state onditions. In the present study, the thermoreeptors temperature and the thermal sensation index are alulated by using the STB model and Eq. (. Fig. illustrates the relation beteen the thermal sensation and the thermoreeptors temperature under steady-state onditions. These data are speified in an appliable range, i.e., 5 ºC < T a < ºC; < V a <.8 m/s; 5% < RH < 75%; < I l <.5 lo;.7 met < M at <.5 met. As shon in Fig., there is an almost linear relation beteen the thermal sensation and the temperature of utaneous thermoreeptors. Hoever, the lines of arm and old onditions do not have a similar slope. In other ords, the arm thermal sensation is more sensitive to the temperature hange of thermoreeptors than the old thermal sensation. Therefore, it an be ritten as follos: = C ( T = C R ( T R n, By using regression analysis on the data presented in Fig., e have and C =.5 and C =.7.M (for.7 < M <.5 (7 T T n, n, = M = M n, (6 (8.685(, =.7 e(, /(,h,.7η e +.685(,h <,,,h,h < η ( here η e is the evaporative effiieny and T =.9( M W 6. ( b, + b, h =.7( M W + T (5 index is based on the ASHRAE -point sale, as follos: +5 intolerable hot, + very hot, + hot, + arm, + slightly arm, neutral sensation, - slightly ool, -, ool, old, - very old, -5 intolerable old [6] Thermoreeptors temperature ( C M =. met M =. met M =.7 met M =.5 met Figure. The relation beteen the thermal sensation and the thermoreeptors temperature under steady-state onditions.

4 Also, under steady-state onditions, the thermal response index an be alulated as follos: Hene, R R = K ( T s s R = K ( T R n C = R C = R n (9 ( By using Eqs. (, ( and (, e an define a ne thermal response index as follos: TABLE I. Case # T air ( C COMPARISON OF TRESP INDEX WITH SIMULATED PMV INDEX AND MEASURED THERMAL SENSATION V air (m/s RH (% M Clo PMV measured thermal sensation, [refrene] TRESP, present study , [] , [] , [] , [] , [] , [] , [] , [] , [] , [] , [] , []. here TRESP = TRESP + TRESP ( K = + d T TRESP min., C( TR Tn, min., ( t R K = + d T TRESP max., C( TR Tn, max., ( t R Eqs. ( represent the human body thermal response onformed to the ASHRAE thermal sensation sale. In the folloing setion, the validation of the ne index ill be disussed under both steady-state and transient onditions. IV. VALIDATION OF THE NEW CRITERION In order to validate the presented riterion inde the simulation results are ompared ith the experimental and simulated data that as reported in the literature [-6]. Sixteen different omparative ases are onsidered to validate the ne index under both steady-state and transient onditions. To validate the presented riterion index under steady-state onditions, telve different omparative ases are onsidered. Table represents a summary of the personal thermal variables and the indoor limate data in the mentioned ases. Moreover, in Table, the TRESP index is ompared ith the simulated PMV index (standard index of ASHRAE [6] for evaluating the thermal sensation under steady-state onditions and also experimental thermal sensation votes [-] in the mentioned steady-state ases. As seen in Table, the TRESP index sho muh better agreement ith published experimental data [, ] than the PMV standard index. It an be seen that the TRESP index is able to predit thermal sensation ith a reasonable auray under steady-state onditions. Furthermore, the average absolute error of TRESP index is approximately.8 in the mentioned steady-state ases. In order to validate the TRESP index under transient onditions, four different omparative ases are onsidered. The first omparison is performed against Arens et al. [5] measured data for a step hange in ambient temperature from.ºc to 6.ºC for an exposure period of 8 min folloed by hour of environment at.7ºc. Fig. shos the TRESP index and the measured thermal sensation [5] under the mentioned onditions. As an be seen in Fig., the results of the present study are in a good agreement ith the experimental results. In the seond ase, the seated subjets ith hot initial thermal sensation ere exposed to ambient air ith 9.6ºC and 5% relative humidity for hours at metaboli rate M =. met. These onditions onform ith empirial onditions of Arens et al. [5] as the validity riterion. In Fig., the value of TRESP index is ompared ith Arens et al. [5] measurements. It an be seen that obtained results from the ne index are in a good agreement ith the mentioned empirial results. As the third and fourth transient ases, the thermal onditions similar to that of Goto et al. [6] ere onsidered. Goto et al. [6] have reported experimental data for thermal sensation of resting human subjets (M = me ho ore a lothing ensemble ith the thermal resistane of.7 lo for an exposure period of 5 min at onstant ambient onditions (6ºC and 5%RH. In the initial onditions, the subjets pereive a hot thermal sensation about.7 due to their high ativity metaboli rate Arens et al. [5] Figure. Comparison of experimental data of Arens et al. [5] and simulated results of the present study for thermal sensation.

5 Arens et al. [5] Measurement (Goto et al. [6] Figure. Comparison of the presented TRESP index and measured thermal sensation [5] at ambient onditions 9.6ºC/5%RH In Fig. 5, the simulated TRESP index is ompared ith the measured data of Goto et al. [6]. Also, Fig. 6 shos the measured data of Goto et al. [6] and the TRESP index ith the initial thermal sensation of.. As an be seen in Figs. 5 and 6, the results of the presented index are in a good agreement ith the published empirial data. It is orth pointing out that the mean absolute errors beteen the ne index and the empirial thermal sensation in the mentioned transient ases are, respetively,.,.,.8 and.6. Therefore, the ne index is able to predit the thermal sensation of the human body ith a reasonable auray under transient onditions V. CONCLUSION In this paper, a ne riterion index for evaluating the human body thermal sensation as introdued on the basis of thermal response of the utaneous thermoreeptors. This index is in onformity ith the ASHRAE standard thermal sensation sale and also ith the physiology of thermal sensation. The mentioned index has been validated against the published experimental data, here a good agreement has been found. Despite its simpliity, the presented index is able to aurately predit the thermal sensation of the body based on the thermoreeptors stati and dynami responses. The validations also sho that the preditions of the ne index are suffiiently reliable under both steady-state and transient onditions. Measurement (Goto et al. [6] Figure 5. Comparison of measured thermal sensation of Goto et al. [6] and simulated results of the present study (third transient ase. Figure 6. Comparison of measured thermal sensation of Goto et al. [6] and simulated results of the present study (fourth transient ase. REFERENCES [] Y.-G. Lv and J. Liu, "Interpretation on thermal omfort mehanisms of human bodies by ombining Hodgkin-Huxley neuron model and Pennes bioheat equation," Forshung im Ingenieuresen, vol. 69, pp. -, 5. [] F. Xu, et al., "Biothermomehanis of skin tissues," Journal of Mehanis and Physis of Solids, vol. 56, pp , 8. [] H. Zhang, "Human thermal sensation and omfort in transient and nonuniform thermal environments," PhD Thesis, University of California, Berkeley,. [] J. W. Ring and R. de Dear, "Temperature Transients: A Model for Heat Diffusion through the Skin, Thermoreeptor Response and Thermal Sensation," Indoor Air, vol., pp. 8-56, 99. [5] H. Hensel, Thermoreeption and temperature regulation. London: Aademi Press, 98. [6] ASHRAE, "ASHRAE handbook of fundamentals," ed Atlanta: ASHRAE,. [7] Y.-G. Lv and J. Liu, "Effet of transient temperature on thermoreeptor response and thermal sensation," Building and Environment, vol., pp , 7. [8] J. W. Ring, et al., "Human thermal sensation: frequeny response to sinusoidal stimuli at the surfae of the skin," Energy and Buildings, vol., pp , 99. [9] R. J. de Dear, et al., "s Resulting From Sudden Ambient Temperature Changes," Indoor Air, vol., pp. 8-9, 99. [] A. Zolfaghari and M. Maerefat, "A ne simplified thermoregulatory bioheat model for evaluating thermal response of the human body to transient environments," Building and Environment, vol. 5, pp ,. [] K. Cena and R. J. De Dear, "Thermal omfort and behavioural strategies in offie buildings loated in a hot-arid limate," Journal of Thermal Biology, vol. 6, pp. 9-,. [] J. Han, et al., "Field study on oupants thermal omfort and residential thermal environment in a hot-humid limate of China," Building and Environment, vol., pp. -5, 7. [] W. A. Andreasi, et al., "Thermal aeptability assessment in buildings loated in hot and humid regions in Brazil," Building and Environment, vol. 5, pp. 5,. [] G. Zhang, et al., "Thermal omfort investigation of naturally ventilated lassrooms in a subtropial region," Indoor and Built Environment, vol. 6, pp. 8-58, 7. [5] E. Arens, et al., "Partial- and hole-body thermal sensation and omfort- - Part I: Uniform environmental onditions," Journal of Thermal Biology, vol., pp. 5-59, 6. [6] T. Goto, et al., "Thermal sensation and thermophysiologial responses to metaboli step-hanges," International journal of Biometeorology, vol. 5, pp., 6.