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Numerical Simulation of the Effects ofBlood Perfusion, Water Diffusion, andVaporization on the Skin Temperatureand Burn InjuriesMing Fu a , Wenguo Weng a & Hongyong Yuan aa Institute of Public Safety Research, Department of EngineeringPhysics , Tsinghua University , Beijing , P.R. ChinaPublished online: 17 Mar 2014.

To cite this article: Ming Fu , Wenguo Weng & Hongyong Yuan (2014) Numerical Simulation of theEffects of Blood Perfusion, Water Diffusion, and Vaporization on the Skin Temperature and BurnInjuries, Numerical Heat Transfer, Part A: Applications: An International Journal of Computation andMethodology, 65:12, 1187-1203, DOI: 10.1080/10407782.2013.869449

To link to this article: http://dx.doi.org/10.1080/10407782.2013.869449

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Numerical Heat Transfer, Part A, 65: 1187–1203, 2014Copyright © Taylor & Francis Group, LLCISSN: 1040-7782 print/1521-0634 onlineDOI: 10.1080/10407782.2013.869449

NUMERICAL SIMULATION OF THE EFFECTS OF BLOODPERFUSION, WATER DIFFUSION, AND VAPORIZATIONON THE SKIN TEMPERATURE AND BURN INJURIES

Ming Fu, Wenguo Weng, and Hongyong YuanInstitute of Public Safety Research, Department of Engineering Physics,Tsinghua University, Beijing, P.R. China

Skin burn induced by thermal radiation or heat source is one of the common butsevere, injuries in firefighting and some industry work exposed to intensive radiation.In this article, a multi-layer skin model on heat and mass transfer is presented articleto investigate the effects of blood perfusion, water diffusion, and vaporization on tissuetemperature and skin burn after removing the heat source. The numerical results of themodel are in good agreement with previous experimental results. A parametric study iscarried out to investigate the effects of skin geometrical and thermal parameters, andinitial tissue temperature on skin temperature distribution and burn injuries after theremoval of the heat source. The results show two-sided effects on tissue temperature, i.e.,heat loss due to water vaporization and water diffusion can cool the epidermis; however,blood perfusion and water diffusion heat the subcutaneous tissue incurring skin damage.It is found that the epidermis and dermis thickness, the dermal and subcutaneous tissuethermal conductivity, and the subcutaneous tissue heat capacity have significant impacton tissue temperature and burn injuries, while the epidermis thermal conductivity, theepidermis and dermis heat capacity, the blooding perfusion rate, and the water diffusivityhave little influence.

1. INTRODUCTION

Fire fighters and other personnel exposed to the threat of intensive radiationor heat source are subjected to intense high temperatures and other extremehazardous environments [1]. Without proper protective garment and equipment, skinburn of life-threatening injury usually occurs during firefighting and some industrywork [2–4]. Skin, the largest human organ, helps to regulate core temperatureduring thermoregulation and serves to maintain water balance in metabolism [5].The prediction of the severity of skin burn, ranking the level by first, second, orthird degree, is based on the damaged depth of the skin layers. It is very difficult toevaluate in a clinical setting.

Received 13 April 2013; accepted 7 November 2013.Address correspondence to W.G. Weng, Institute of Public Safety Research, Department of

Engineering Physics, Tsinghua University, Beijing, 100084, P.R. China. E-mail: wgweng@tsinghua.edu.cn.

Color versions of one or more of the figures in this article can be found online at www.tandfonline.com/unht.

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1188 M. FU ET AL.

NOMENCLATURE

cp specific heat, (J/kg�C) �x distance from current tissue positionDf coefficient of water diffusion in to body core, (m)

tissue, (m2/s) � average distance of the momentumk thermal conductivity, (W/m�C) boundary layer, (m)M molar mass of water, � water content, (%)

(18 g/mol) � skin density, (kg/m3�

P pre-exponential factor, (1/s), � blood perfusion rate, (m3/s m3)or vapor pressure of water, (Pa) � damage function

Q volumetric heat source, (W/m3)R universal gas constant, (8.314J/mol�C) Subscripts and SuperscriptsRH relative humidity, (%) a airT temperature, (�C) b bloodt time, (s) c corex space coordinate, (m) f water diffusion�E activation energy of skin, (J/kmol) m metabolic production�Hvap enthalpy of vaporization of water, s skin surface

(2408J/kg) v vaporization�m rate of water vaporization from the w water

skin surface, (g/m2 s)

Over the past decades, research has been conducted on skin burn predictionin two ways: numerical computations with bioheat models [6–13], and experimentalstudies using an instrumented manikin test subjected to a simulated flash fire orthermal radiation [2, 14–15]. An analytical bioheat model was initially developedfrom Pennes [6] with blood perfusion, followed by a finite element model fromDiller and Hayes [7]; one-dimensional finite difference and two-dimensional finiteelement bioheat models developed by Ng and Chua [8,9] and a multi-layer modelthat couples heat and moisture transport of protective fabrics under flash fireconditions developed by Song et al. [10,11]; to a finite volume model consisting ofthree parts from the skin to a fire-resistant fabric to simulate the heat transfer inprotective clothing developed by Ghazy and Bergstrom [12,13]. The models of Ngand Chua are mesh-independent to investigate thermal phenomena during the injuryprocess exposed to various burning conditions. Juricic et al. [14] presented a model-based system recording temperature from an instrumented manikin with protectivegarments to evaluate skin burn subjected to flash fire.

Subsequent researchers have used the above models to investigate the effectson injury evaluation of sensitivity analysis of tissue properties such as the initial skintemperature and rate of blood perfusion [16], thermal conductivity [17], specific heat[17], geometrical dimensions [18], and convective heating coefficient [19], etc. Theseanalyses have been performed to determine which parameters or their interactionshave a great effect on skin temperature prediction and injury assessment. However,the above skin models and their applications mainly focus on the heat transferprocess, without considering water diffusion and vaporization within the humanskin that are crucial to temperature regulation of the skin [20–23]. The heat andmass transfer by diffusion and vaporization between the epidermis and the dermis is

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NUMERICAL SIMULATION ON THE SKIN TEMPERATURE 1189

essential to providing nutrients and conducting energy because of no bleeding in theepidermis.

This article develops a multi-layer model on skin heat and mass transfer,considering the effects of blood perfusion, water diffusion, and vaporization. Basedon this model, the effects of blood perfusion, water diffusion, and vaporization ontissue temperature are analyzed after termination of the exposure to heat source.The effects of skin parameters and initial tissue temperature on tissue temperatureand burn injuries are also tested. Section 2 presents the details of a bioheat model.Numerical solution of the model is given in section 3. Section 4 shows results anddiscussion, followed by the conclusion.

2. SKIN MODEL ON HEAT AND MASS TRANSFER

A multi-layer model on skin heat and mass transfer is established to simulatethe thermal behaviors of skin tissue. The geometry of skin used in this model isshown in Figure 1. The skin composes of three layers: the epidermis, the dermis, andthe subcutaneous tissue. Each layer is assumed to be homogeneous. The values ofskin thermal parameters, including blood perfusion rate, thermal conductivity, andheat capacity, might change with time when exposed to the heat source. Since it isdifficult to predict them during high temperature, those thermal parameters in eachskin layer are assumed to be constant.

Pennes-bioheat equation [6] is one of the most used models to simulate thethermal behaviors of skin tissue, including blood perfusion and metabolic heatgeneration. Shen et al. [22] considered the heat and mass transfer with waterdiffusion and vaporization in a skin model. However, these two ways within thethree skin layers are different, which is not considered in Shen’s model [22]. Waterdiffusion and metabolic heat generation remain in all three layers; there is no bloodperfusion in the epidermis. Although water within the skin tissue could vaporizedepending on the skin temperature, water vaporization occurs only on the surface ofthe epidermis [24]. With the above considerations of skin geometrical and thermalphysiology, a multi-layer skin model on heat and mass transfer including bloodperfusion, water diffusion and vaporization can be written as follows.

Epidermis � �cpT

t+Qd+Qv = k

2T

x2+Qm 0 < x < x1 (1)

Dermis � �cpT

t+Qd = k

2T

x2+ bcpb�b �Tb − T�+Qm x1 < x < x2 (2)

Subcutaneous � �cpT

t+Qd = k

2T

x2+ �bcpb�b �Tb − T�+Qm x2 < x < x3 (3)

Qv =�m • �Hvap

�(4)

�m = D

M

R

(Pw

Tw

)s

−(Pw

Tw

)a

× RH

�(5)

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1190 M. FU ET AL.

Figure 1. Schematic diagram of three-layer skin.

Qd = Dfcpw ��s − �c� �T − Tc�

��x�2(6)

Water transport in skin is stimulated by the Fick’s law of diffusion.

�w

t= Dw

(2�w

x2

)(7)

Here Qv, Qd, and Qm are the volumetric heat loss due to water vaporization, waterdiffusion, and metabolic production, respectively. Compared with the involved heatfluxes, Qm is considered as zero. �, cp, k, and T are the density, specific heat, thermalconductivity, and temperature of skin, respectively. �b, cpb, �b, and Tb are the density,specific heat perfusion rate and temperature of blood, respectively. �b is taken as1060kg/m3, and cpb is taken as 3770J/(kg�C) [18]. Tb is assumed to have the samevalue of the core temperature Tc (set as 37

�C). �m is the rate of water vaporizationfrom the skin surface. �Hvap is the enthalpy of vaporization of water, taken as

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NUMERICAL SIMULATION ON THE SKIN TEMPERATURE 1191

2408J/kg. From the assumption that the boundary layer between the outer skinsurface and the air layer is a steady–state condition introduced by Duncan et al. [24],Eq. (5) is developed to describe the water diffusion due to a water vapor gradient.Dv is the average water vapor diffusivity in the boundary layer, taken as 2�6× 10−10

m2/s [22]. M is the molar mass of water, taken as 18g/mol. R is the universalgas constant, taken as 8.315J/(mol�C). RH is the relative humidity of the air. � isthe average of the momentum boundary layer, the solving of which is accordingto references [22, 24]. Equation (6) was developed by Shen et al. [22], based onthe coupled driving force for fluid flow from the water concentration differencebetween the skin surface and the core body, and the skin temperature differencebetween the current tissue position and the core body. Df is the coefficient of waterdiffusion in tissue, taken as 5× 10−10 m2/s, and cpw is the specific heat of water,taken as 4200J/(kg�C) [22]. �s and �c is the water content on the skin surface andcore body, respectively. The values of thermal physical properties of three layers aresummarized and listed in Table 1.

Skin damage will begin to occur when the temperature of the basal epidermisor dermis reaches 44�C [28]. According to the process of a first-order chemicalreaction,

d�

dt=

{0 T < 44�C

Pe−(�ERT

)T ≥ 44�C

(8)

Damage function � reaches the values of 0.53, 1.0, and 104 corresponding to thefirst-, second-, and third-degree, respectively [29]. Values of P and �E are chosenaccording to Weaver and Stoll [30] for the prediction of skin burn.

The initial temperature distribution in the studies [16, 18] was a lineardistribution between 32.5�C at the epidermis surface and 37�C at the subcutaneousbase (core body temperature). This initial condition is also used in our model.A uniform initial skin temperature of 34�C was also used in the studies in references[12, 16, 27], and is engaged in the current study to analyze the effects of initialtemperature on skin burn. The boundary condition on the skin surface has two cases,as follows.

Table 1. Physical and thermal properties of skin

Physical parameter Epidermis Dermis Subcutaneous tissue References

Thickness (mm) 0.04-0.16 (0.08) 1.6-2.8 (2.0) 10 [16, 27]Thermal conductivity 0.21-0.26 (0.24) 0.37-0.52 (0.45) 0.16-021 (0.19) [16, 27](W/m·�C)

Specific heat (Jkg−1k−1� 3578-3600 (3590) 3200-3400 (3330) 2300-3060 (2500) [16, 27]Blood perfusion rate 0 0.006-0.015 0.006-0.015 [16, 17, 27](m3/s/m3� (0.00125) (0.00125)

Density (kg/m3� 1200 1200 1000 [18]Water diffusivity (mm2/s) 2.7×10−4 − 3×10−3 2.7×10−4 − 3×10−3 2.7×10−4 − 3×10−3 [24–26]

(5×10−4� (5×10−4� (5×10−4�

Water content (%) 70 70 20 [24]

*Numbers in parentheses are the commonly used values.

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1192 M. FU ET AL.

For the case of contacting with the heat source of constant temperature, it isassumed that the interface thermal resistance is considered as zero between the skinand the heat source.

T �0� t� = Tconst (9)

For the case exposed to the thermal radiation with constant heat flux,

−T

x

∣∣∣∣x=0

= qconst (10)

The boundary conditions between the three skin layers for Eqs. (1–3) and Eq. (7)are obtained from the continuity of the temperature and the water content betweenthe two adjacent skin layers, respectively.

3. NUMERICAL SOLUTION

A finite volume method is used to solve the above equations to obtaintemperature distribution in multiple layers of skin. A fully implicit time schemeis used to discretize these partial differential equations. The space step is chosenthe same in each layer skin. 20, 40, and 100 grids are used for the epidermis, thedermis, and the subcutaneous tissue, respectively. The time step is chosen as 0.01 sto ensure that the nondimensional change of transient temperature distribution isacceptable. The tridiagonal matrix algorithm scheme [31] is used to solve thosediscretized equations. The solution procedure proceeds as follows. For each timestep, water transport in skin described in Eq. (7) from the previous time step is usedas initial values. The source terms including the volumetric heat loss due to watervaporization and diffusion described in Eqs. (4–6) are updated based on the currentwater content distribution. Next, new temperature distribution is calculated from theouter skin surface to the subcutaneous base with the updated source terms. After thenew skin temperature distribution is obtained, both the basal epidermis and dermistemperatures are used to calculate damage function � (Eq. (10)) to predict times toreceive second- and third-degree skin burn.

4. RESULTS AND DISCUSSION

Validation of our model is first conducted, compared with the existingsimulation results [18] and experimental data [29]. Based on this model, the effectsof blood perfusion, water diffusion, and vaporization on tissue temperature afterremoving the heat source are investigated. The effects of skin properties and initialtissue temperature on tissue temperature and burn injuries after the removal of theheat source are also studied.

4.1. Model Validation

A multi-layer model on skin heat and mass transfer considering the effects ofthe water diffusion and vaporization on skin temperature is developed in section 2,with two kinds of the boundary condition on the skin surface. For the case of

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NUMERICAL SIMULATION ON THE SKIN TEMPERATURE 1193

Figure 2. Comparison of the tissue temperature for a surface temperature of 90�C. (t: Reference data[18]; tn: current numerical results.).

contact with the heat source with a constant temperature, a comparison is madewith the results of Jiang et al. [18] during the injury process exposed to the hotsource, based on Pennes-bioheat equation [6] with blood perfusion and withoutwater diffusion and vaporization. In their study, skin tissue was heated by theheat source with 90�C for 15 s. Geometrical and thermal parameters of the skin inour model are the same with Jiang’s study, shown in the parentheses of Table 1.Comparison with Jiang’s data of skin temperature distribution is shown in Figure 2.The simulated results have the same trends as Jiang’s data. However, the currentnumerical results are 0.3–1.0�C higher than the reference data. It might have thereason that our skin model considers the water diffusion and vaporization withinthe skin layers. These ways may heat the deep skin tissue when contacting with theheat source.

For another case exposed to the thermal radiation with a constant heatflux, Figure 3 shows the comparison of heat flux resulting in the second degreeburn between the experimental of the reference [29] on blackened living skin, andthe simulated results from the current model and Jiang’s model. The standarddeviation and the average relative deviation between the results of our model andthe experimental data of reference [29] are 0.516 and 4.91% less than that of Jiang’sresults (0.989 and 11.70 %), respectively. It can be shown that the difference betweenthe results of the current model and the experimental data is less than that of Jiang’smodel.

In summary of both boundary conditions of constant temperature andconstant heat flux, it is indicated that the current model can be used to simulatethe heat and mass transfer with water diffusion and vaporization in skin tissue, andaccurately evaluate skin injuries contacting with the heat source or exposed to thethermal radiation.

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1194 M. FU ET AL.

Figure 3. Comparison of the heat flux causing the second-degree skin burn.

4.2. Effects of Blood Perfusion, Water Diffusion, and Vaporization

Skin damage after the heat source is removed in a clinical setting might happenbecause of incorrect delayed treatment [33]. Some authors [27] recognized that theskin surface temperatures will decrease substantially after removing the heat source,but did not discuss the effects of blood perfusion, water diffusion and vaporizationon skin tissue and skin burn. The way of experiments on human subjects exposed tohigh heat radiation or hot environments are most correct to study those effects afterremoving the heat source, but this is against the principle of humanity. Based on thepresented model, those effects on tissue temperature after removing the heat sourceare analyzed, to assess the influence of delayed cooling on burn injuries.

In the comparison with the numerical results of Jiang et al. [18], the humanskin is heated with a hot surface with 90�C. After exposure of 15 s, the boundarycondition is set as thermal insulation. Numerical computation of another 80 s isconducted after the removal of the heat source. Figure 4 shows the temperaturedistribution with the depth of the skin layers in different time after the exposureended. It is observed that temperature distribution at the depths below 1.4mm(including the epidermis) is decreasing over time after the exposure ended.Temperatures at the depths between 1.4mm and 2.4mm are augmenting from 0sto 10 s and reducing from 10s to 80 s, while that at the depths between 2.4mmand 3mm are increasing from 0s to 20 s and decreasing from 20s to 80 s. Thetemperature distribution from 3mm to 4mm is rising from 0s to 40 s and droppingfrom 40s to 80 s; however, that of the subcutaneous tissue at the depths above 4mmis increasing after ending the exposure. It is also seen that the temperatures at thedepths between 2.08 mm and 4 mm (within the subcutaneous tissue) are more than44�C, and skin tissues at these depths would be damaged [28]. These results reflectthe two-sided effects of blood perfusion, water diffusion and vaporization after thetermination of the exposure. The temperatures within epidermis are still higher thanthe temperature of core body (37�C) after ending the exposure. Since it is assumed

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NUMERICAL SIMULATION ON THE SKIN TEMPERATURE 1195

Figure 4. Temperature distribution with the depth of the skin layers after ending heat source.

that there is no blood perfusion in the epidermis, heat loss due to water vaporizationand water diffusion can cool the epidermis (Eq. (1)). However, the temperatureswithin the subcutaneous tissue are lower than the temperature of core body (37�C)after ending the exposure. The subcutaneous tissue can be heated by blood perfusionand water diffusion (Eq. (3)), incurring skin damage. During the early post-burnperiod, the methods of near infrared reflectance spectroscopy and imaging [34] andlaser Doppler imaging [35] are used to determine the depth of burn injuries caused bythe heat source. However, the water content is difficult to assess by current clinicalobservation [34]. The evaluation of local burn injury in the deep subcutaneous tissue,incurred by the heat transfer by blood perfusion, diffusion, and vaporization afterremoving the heat source is not accurately quantified. Therefore, the treatment ofskin burn during the early post-burn period should put the emphasis on detectingthe skin temperature and water content distribution, not only on the damage depth.

It can be shown that dealing with skin injury from touching a heat surfaceor steam in a clinical setting would need much care to prevent skin damage in thedeeper tissue after removing the heat source.

4.3. Effects of Geometrical and Thermal Parameters

The effects of skin tissue properties including geometrical and thermalparameters and the initial skin temperature on injury evaluation have beenperformed [16–19], without considering water diffusion and vaporization within thehuman skin after the removal of the heat source. These tissue properties include thethicknesses, the thermal conductivity, the specific heat, the blooding perfusion rateand the water diffusivity, which are not constant depending on the position on thehuman or the subject [27]. The values most commonly used in the references aretaken as the base values. The ranges chosen and their base values of thermal physicalproperties are listed in Table 1.

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1196 M. FU ET AL.

Figure 5. Skin temperature distributions at 10 s and 20 s after removing the heat source for differentdermis and epidermis thickness. (a) Different epidermis thickness with a dermis thickness of 2.0mm;and (b) different dermis thickness with an epidermis thickness of 0.08mm.

In this section, the effects of tissue properties on tissue temperature andburn injuries after ending the exposure to heat source are investigated, shown inFigure 5–8.

The effects of varying values for different epidermis and dermis thicknesson temperature are tested. The transient temperature distributions in 10 s and 20 safter removing heat source for different epidermis and dermis thickness are shownin Figure 5. The different subcutaneous tissue thickness is not considered becauseits influence on the heat conduction in the skin is minimal [17]. It can be seenfrom Figure 5 that the epidermis and dermis thickness have an impact on thetransient temperature distributions. Tissue temperatures within the epidermis anddermis decrease with the increasing epidermis and dermis thickness, especially at thecondition of different epidermis thickness from 0.12mm to 0.16mm with the dermisthickness of 2.0mm. However, the deep subcutaneous tissue temperature remainsconstant. From Figure 5a with the dermis thickness of 2.0mm, tissue temperatureswithin the epidermis and dermis are closely aligned with the increasing epidermisthickness from 0.04mm to 0.12mm. The reason for this phenomenon is difficult tointerpret in our study field, which might be an important scientific basis for heatand mass transfer in skin tissue in future study. Therefore, skin model developmentshould have similar epidermis and dermis thickness to ensure the prediction accuracyof the tissue temperature. It is indicated that skin damage treatment after the heatsource is removed in a clinical setting might lay emphasis on the epidermis anddermis, not on the deep subcutaneous tissue due to not substantially effect.

The effects of varying thermal conductivity in three layers on skin temperatureafter removing the heat source are also analyzed. The transient temperatures of thebasal epidermis and dermis are used as injury threshold to verdict if skin damageoccurs [28]. These two temperatures after removing heat source for different valuesof the thermal conductivity are shown in Figure 6. From Figure 6a, it can beobserved that the variation of the epidermis thermal conductivity has no influenceon the prediction of the injury threshold. Figure 6b shows that the increase of thethermal conductivity of the dermis results in the increase of these two temperatures.Absorbed heat at the epidermal-dermal interface is more easily transferred todeeper skin with the increasing dermal thermal conductivity, and therefore requiresless time to reach the injury threshold. Surprisingly, the results obtained fromFigure 6c are contrary to the effects of dermal thermal conductivity. The effect of

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NUMERICAL SIMULATION ON THE SKIN TEMPERATURE 1197

Figure 6. Effect of the thermal conductivity on temperatures of the basal epidermis and dermis afterremoving the heat source (unit: W/m�C). (a) Epidermis, (b) dermis, and (c) subcutaneous tissue.

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1198 M. FU ET AL.

Figure 7. Effects of the specific heat on temperatures of the basal epidermis and dermis after removingthe heat source (unit: J/kg�C). (a) Epidermis, (b) dermis, and (c) subcutaneous tissue.

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NUMERICAL SIMULATION ON THE SKIN TEMPERATURE 1199

Figure 8. (a) Effects of the blooding perfusion rate and (b) the water diffusivity on temperatures ofthe basal epidermis and dermis after removing the heat source.

the subcutaneous tissue thermal conductivity is smaller as its thickness is larger.With the increase of the subcutaneous tissue thermal conductivity, the subcutaneoustissue absorbs more easily heat from the epidermis and dermis. Therefore, these twotemperatures are reducing for the same boundary condition with removing the heatsource.

The effects of varying values for the specific heat in three layers are alsoinvestigated on transient temperatures of the basal epidermis and dermis after thedirect exposure has ended, and the results are illustrated in Figure 7. It showsthat variation of the specific heat in the epidermis and the dermis has no impacton predicting skin injury threshold. Figure 7c indicates that these two transienttemperatures decrease with the increase of the specific heat of the subcutaneoustissue. Because the thickness of the subcutaneous tissue is larger, it needs toabsorb more heat from the epidermis and the dermis to raise its temperature whenincreasing its specific heat. Therefore, the heat capacity of the subcutaneous tissueplays an important role in preventing skin injuries.

The effects of variations of the blood perfusion rate in the dermis andsubcutaneous layers and the water diffusivity in skin on the above two transienttemperatures are shown in Figure 8. The results show that variations of the bloodperfusion rate have no obvious influence on the injury threshold, which is similarto the results of Ng and Chua [16]. It is also shown that the variations of waterdiffusivity have not obvious effects on the injury threshold. However, there is notshown that the effects of the water diffusion and vaporization considered in the

Table 2. Time to the second-degree and third-degree skinburn for various heat sources with different initial skintemperature distributions

Heat source (�C) 90 120 150

Linear distribution between 32.5�C and 37�CTime to second skin burn (s) 0.30 0.13 0.09Time to third-degree skin burn (s) 5.06 0.60 0.25Uniform temperature of 34�CTime to second skin burn (s) 0.28 0.13 0.09Time to third-degree skin burn (s) 4.95 0.58 0.24

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1200 M. FU ET AL.

Table 3. Time to the second-degree and third-degree skinburn for various radiant heat fluxes with different initial skintemperature distributions

Radiant heat flux (kW/m2� 20 30 40

Linear distribution between 32.5�C and 37�CTime to second skin burn (s) 3.40 1.91 1.28Time to third-degree skin burn (s) 11.32 5.84 3.68Uniform temperature of 34�CTime to second skin burn (s) 3.16 1.78 1.20Time to third-degree skin burn (s) 10.92 5.63 3.55

current model have less effects on skin temperature. From Figure 2, the temperatureof the basal epidermis calculated in the presented model is approximately 0.6�Chigher than that of the data of Jiang et al. [18] without considering water diffusionand vaporization. Skin damage will be predicated at an earlier time to take effectivemedical treatment. Therefore, the results from Figure 8 show that the variations ofwater diffusivity can be ignored in the treatment of skin burn after removing theheat source, not the effects of water diffusion and vaporization.

4.4. Effects of Initial Tissue Temperature

The effects of varying initial tissue temperature on the skin burn prediction aretested. For two kinds of the boundary condition, the time to the second- and third-degree skin burns with different initial skin temperature distributions are shown inTables 2 and 3, respectively. The lowest and highest values of the heat sources andradiant heat fluxes during firefighting are summarized based on the studies [1,2,32]and are used as different boundary conditions. From Table 2 of various heat sources,it can be observed that there is no pronounced difference of the time to the second-degree skin burn between using a uniform tissue temperature of 34�C and using alinear temperature distribution from 32.5�C to 37�C; however the time to the third-degree skin burn using the linear distribution is higher than that using the uniformtemperature. Table 3 of radiant heat fluxes reflects higher values of the time to thesecond- and third-degree skin burn using the linear distribution. Therefore, theseresults indicate that the initial temperature of the skin tissue affects the outcome ofskin burn evaluation. It would suggest using the uniform skin temperature of 34�C asthe initial condition because its prediction of burn injuries is a conservative estimate.

5. CONCLUSION

A finite volume model for transient heat and mass transfer within the multi-layer skin, considering the effects of water diffusion and vaporization on skintemperature, is developed. Comparing to the numerical results in the previousliteratures, those of our model agree better with previous experimental results. Themodel is employed to study the effects of blooding, water diffusion, and vaporizationon the tissue temperature after removing the heat source, to assess the influenceof delayed cooling on burn injuries. The results indicate two-sided effects on tissue

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temperature, i.e., heat loss due to water vaporization and water diffusion can coolthe epidermis, however, blood perfusion and water diffusion heat the subcutaneoustissue incurring skin damage.

The effects of skin tissue properties on tissue temperature and burn injuriesafter removing the heat source are also tested. The results show that the epidermisand dermis thickness only has a significant impact on the epidermis and dermistemperatures; however, the deep subcutaneous tissue temperature remains constant.The transient temperatures of the basal epidermis and the basal dermis are affectedby the dermal and subcutaneous tissue thermal conductivity, and the subcutaneoustissue heat capacity. It is also found that the epidermis thermal conductivity, theepidermis and dermis heat capacity, blooding perfusion rate, and water diffusivityhave no obvious influence on injury threshold.

The above findings can provide appropriate information and give somesuggestion to burn diagnosis, prediction, and evaluation for skin damage afterremoving the heat source. In a general context, the methods and results in this studycan also be used to study heat and mass transfer in the human skin. In future study,the model will be used to integrate with protective clothing and air gap systemsduring a wide range of exposure conditions with high temperatures and heat fluxes,providing insight into the physics of heat and mass transfer in the human body-clothing- environment system.

FUNDING

This study was supported by the National Natural Science Foundation ofChina (grant nos. 51076073, 91024018, and 91024024) and the National BasicResearch Program of China (973 Program) (grant no. 2012CB719705). The authorsare deeply grateful for their support.

REFERENCES

1. I. Holmer and D. Gavhed, Classification of Metabolic and Respiratory Demands in FireFighting Activity with Extreme Workloads, Appl. Ergon., vol. 38, pp. 45–52, 2007.

2. M. A. Camenzind, D. J. Dale, and R. M. Rossi, Manikin Test for Flame EngulfmentEvaluation of Protective Clothing: Historical Review and Development of a New ISOStandard, Fire Mater., vol. 31, pp. 285–295, 2007.

3. G. Havenith, Individualized Model of Human Thermoregulation for the Simulation ofHeat Stress Response, J. Appl. Physiol., vol. 90, pp. 1943–1954, 2001.

4. I. Holmer, Protective Clothing in Hot Environments, Ind. Health, vol. 44, pp. 404–413,2006.

5. E. R. Nadel, R.W. Bullard, and J. A. Stolwijk, Importance of Skin Temperature inRegulation of Sweating, J. Appl. Physiol., vol. 31, pp. 80, 1971.

6. H. H. Pennes, Analysis of Tissue and Arterial Blood Temperatures in Resting HumanForearm, J. Appl. Physiol., vol. 1, pp. 93–122, 1948.

7. K. R. Diller and L. J. Hayes, A Finite Element Model of Burn Injury in Blood-PerfusedSkin, J. Biomech. Eng., vol. 105, pp. 300–307, 1983.

8. E. Y. K Ng and L. T. Chua, Prediction of Skin Burn Injury, Part 1: NumericalModelling, P. I. Mech. Eng. H, vol. 216, pp. 157–170, 2002.

9. E. Y. K Ng and L. T. Chua, Comparison of One- and Two-dimensional Programmesfor Predicting the State of Skin Burns, Burns, vol. 28, pp. 27–34, 2002.

Dow

nloa

ded

by [

McM

aste

r U

nive

rsity

] at

06:

15 3

0 O

ctob

er 2

014

1202 M. FU ET AL.

10. G. W. Song, R. L. Barker, H. Hamouda, A. V. Kuznetsov, P. Chitrphiromsri, and R. V.Grimes, Modeling the Thermal Protective Performance of Heat Resistant Garments inFlash Fire Exposures, Text. Res. J., vol. 74, pp. 1033–1040, 2004.

11. G. W. Song, P. Chitrphiromsri, and D. Ding, Numerical Simulations of Heat andMoisture Transport in Thermal Protective Clothing under Flash Fire Conditions, JOSE,vol. 14, pp. 89–106, 2008.

12. A. Ghazy and D. J. Bergstrom, Numerical Simulation of Transient Heat Transfer in aProtective Clothing System during a Flash Fire Exposure. Numer. Heat Transfer A., vol.58, pp. 702–724, 2010.

13. A. Ghazy and D. J. Bergstrom, Numerical Simulation of Heat Transfer in Firefighters’Protective Clothing with Multiple Air Gaps during Flash Fire Exposure, Numer. HeatTransfer A., vol. 61, pp. 569–593, 2012.

14. D. Juricic, B. Musizza, M. Gasperin, I. Mekjavic, M. Vrhovec, and G. Dolanc,Evaluation of Fire Protective Garments by using Instrumented Mannequin and Model-based Estimation of Burn Injuries, Proc. 15th Mediterranean Conference on Control &Automation, pp. 1–6, Athens, Greece, 2007.

15. R. M. Rossi, G. Bruggmann, and R. Stampfli, Comparison of Flame Spread of TextilesAnd Burn Injury Prediction with a Manikin, Fire Mater., vol. 29, pp. 395–406, 2005.

16. E. Y. K Ng and L. T. Chua, Prediction of Skin Burn Injury, Part 2: Parametric andSensitivity Analysis, P. I. Mech. Eng. H, vol. 216, pp. 171–183, 2002.

17. M. Gasperin and D. Juricic, The Uncertainty in Burn Prediction as a Result of VariableSkin Parameters: An Experimental Evaluation of Burn-protective Outfits, Burns, vol. 35,pp. 970–982, 2009.

18. S. C. Jiang, N. Ma, H. J. Li, and X. X. Zhang, Effects of Thermal Properties andGeometrical Dimensions on Skin Burn Injuries,Burns, vol. 28, pp. 713–717, 2002.

19. L. Autrique, and C. Lormel, Numerical Design of Experiment for Sensitivity Analysis—Application to Skin Burn Injury Prediction, IEEE T Bio-Med. Eng., vol. 55, pp. 1279–1290, 2008.

20. A. B. Goodman and A. V. Wolf, Insensible Water Loss From Human Skin as a Functionof Ambient Vapor Concentration, J. Appl. Physiol., vol. 26, pp. 203–207, 1969.

21. Y. Houdas, J. Timbal, C. Boutelie, J. D. Guieu, and J. Colin, Skin Temperatures inWarm Environments and Control of Sweat Evaporation, J. Appl. Physiol., vol. 33, pp.99–104, 1972.

22. W. S. Shen, J. Zhang, and F. Q. Yang, Skin Thermal Injury Prediction with StrainEnergy, Int. J. Nonlin. Sci. Num., vol. 6, pp. 317–328, 2005.

23. A. H. Mao and Y. Li, Numerical Heat Transfer Coupled with Multidimensional LiquidMoisture Diffusion in Porous Textiles with a Measurable-Parameterized Model, Numer.Heat Transfer A., vol. 56, pp. 246–268, 2009.

24. J. M. Duncan, C. E. David, and A. Richard, Dynamic Simulations of Tissue Welding,Proc. SPIE, vol. 2671, pp. 234–242, 1996.

25. L. L. Latour, K. Svoboda, P. P. Mitra, and C. H. Sotak, Time-Dependent Diffusion ofWater in a Biological Model System, P. Natl. Acad. Sci. USA, vol. 91, pp. 1229–1233,1994.

26. A. Szafer, J. H. Zhong, and J. C. Gore, Theoretical-Model for Water Diffusion inTissues, Magn. Reson. Med., vol. 33, pp. 697–712, 1995.

27. N. N. Johnson, J. P. Abraham, Z. I. Helgeson, W. J. Minkowycz, and E. M. Sparrow,An Archive of Skin-Layer Thicknesses and Properties and Calculations of Scald Burnswith Comparisons to Experimental Observations, J. Therm. Sci. Eng. Appl., vol. 3, pp.1–9, 2011.

28. F. C. Henriques and A. R. Moritz, Studies of Thermal Injuries I: The Conduction ofHeat to and through Skin and the Temperatures Attained Therein, A Theoretical andExperimental Investigation, Am. J. Pathol., vol. 23, pp. 531–549, 1947.

Dow

nloa

ded

by [

McM

aste

r U

nive

rsity

] at

06:

15 3

0 O

ctob

er 2

014

NUMERICAL SIMULATION ON THE SKIN TEMPERATURE 1203

29. A. M. Stoll and M. A. Chianta, Method and Rating System for Evaluation of ThermalProtection, Aerospace Med., vol. 40, pp. 1232–1237, 1969.

30. J. A. Weaver and A. M. Stoll, Mathematical Model of Skin Exposed to ThermalRadiation, Aerospace Med., vol. 40, pp. 24–30, 1969.

31. W. Q. Tao, Numerical Heat Transfer, 2nd ed., pp. 99–104, Xi’an Jiaotong University,Xi’an, 2001. (In Chinese).

32. R. Rossi, Fire Fighting and its Influence on the Body, Ergonomics, vol. 46, pp. 1017–1033, 2003.

33. D. L. Carlson, D. L. Maass, J. White, P. Sikes, and J. W. Horton, Caspase InhibitionReduces Cardiac Myocyte Dyshomeostasis and Improves Cardiac Contractile Functionafter Major Burn Injury, J. Appl. Physiol., vol. 103, pp. 323–330, 2007.

34. M. G. Sowa, L. Leonardi, J. R. Payette, and J. S. Fish, Near Infrared SpectroscopicAssessment of Hemodynamic Changes in the Early Post-Burn Period, Burns, vol. 27, pp.241–249, 2001.

35. H. Hoeksema, K. Sijpe, T. Tondu, M. Hamdi, K. Landuyt, and P. Blondeel, Accuracy ofEarly Burn Depth Assessment by Laser Doppler Imaging on Different Days Post Burn,Burns, vol. 35, pp. 36–45, 2009.

Dow

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ded

by [

McM

aste

r U

nive

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] at

06:

15 3

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ctob

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