Queima pele humana

NUMERICAL STUDY ON THE TEMPERATUREPROFILES AND DEGREE OF BURNS IN HUMAN SKINTISSUE DURING COMBINED THERMAL THERAPY

Ik-Tae Im1, Suk Bum Youn1, and Kyounghwa Kim2

1Department of Mechanical Design Engineering, College of Engineering,Chonbuk National University, Jeonju, Republic of Korea2Nano Solution Inc., Jeonju, Republic of Korea

In this study, the temperature distribution in human dermal tissues and possible burns

as a result of local heating of the skin were analyzed numerically. In order to obtain the

temperature profiles of the dermis, fat, and muscle layers, we solved the Pennes bio-heat

equation whose source term was for heat exchange between blood and tissues. The degree

of each burn was predicted by an Arrhenius-type damage function. Two boundary

conditions, namely constant heat flux and constant temperature, were considered as heating

methods. Skin temperature regulation by on/off repetition of heat flux was also considered

as a boundary condition. Time-dependent increases in tissue temperature under constant

heat flux were determined for the skin. Temperature profiles showed different slopes at each

layer due to different thermophysical properties and blood perfusion. Constant temperature

heating up to 320 K for 10 minutes did not cause a burn injury according to our results.

The results also showed that burns can be avoided by controlling the skin temperature under

320 K. Taken together, our results showed that a high heat flux over a short heating period

is safer than a low heat flux over a long heating period.

1. INTRODUCTION

Thermal therapy is a therapeutic method that makes use of thermal sourcessuch as microwave and infrared energy to improve blood flow by increasingthe temperature of the therapy site, thereby relieving fatigue of nerves and musclesas well as increasing the metabolism or necrosis of diseased tissues. Methodsthat may be called ‘‘thermal therapies’’ are often observed around us, and includeapplying a hot compress and far-infrared radiation. These methods are also expectedto improve metabolism by increasing the temperature of the therapy site. Whole-body hyperthermia [1, 2] is an example of active thermal therapy used for treatmentof tumors and cancer. For example, whole-body hyperthermia for tumor treatmentnot only is intended to increase metabolism, but also utilizes the principle in which

Received 17 October 2013; accepted 13 August 2014.

Address correspondence to Ik-Tae Im, Chonbuk National University, 567 Baekjedaero,

Duckjin-gu Jeonju, 561-756 Republic of Korea. E-mail: [email protected]

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

com/unht.

Numerical Heat Transfer, Part A, 67: 921–933, 2015

Copyright # Taylor & Francis Group, LLC

ISSN: 1040-7782 print=1521-0634 online

DOI: 10.1080/10407782.2014.955338

921

tumor cells necrotize faster than normal cells at high temperature. The methodis widely used for clinical purposes.

The temperature profile of human tissue heated by thermal therapy is thesubject of medical and engineering interests. For analyses of temperature profilesin human tissue, most studies utilize the bio-heat equation described by Pennes[3], who conducted temperature measurement experiments using human forearms.Although the equation is very simple, studies have obtained relatively satisfactorysolutions using the bio-heat equation [4]. Yuan et al. [5] reported the effect ofperfusion rate on temperature response according to heating of the skin in a studyof heat transfer in human subcutaneous tissue. Several other studies [6–8] have usedthe bio-heat equation to show skin tissue temperature response characteristics duringcyclical heating. Importantly, these skin response characteristic can be applied toidentify the positions of subcutaneous tumors [9, 10].

In this study, the temperature profiles and possibility of burns in human skintissue with the local heating of the skin were investigated in order to obtain basicdata on the heat transfer phenomenon in human skin tissue necessary for thedevelopment of a combined thermal therapy device using heat and light. Figure 1shows a photograph of the prototype of a combined therapy device utilizing infrared

NOMENCLATURE

A pre-exponential factor (1=s)

c specific heat (J=kg K)

h enthalpy

k thermal conductivity (W=m K)

qm metabolic heat generation

R universal gas constant

(8.3143 J=mol K)

r radial coordinate

T temperature (�C, K)

t time (s)

x axial coordinate

DE activation energy (J=mol)

q density (kg=m3)

X damage function

x blood perfusion rate (1=s)

Subscript

b blood

Figure 1. Prototype of the combined heat and light therapy device.

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heat and white light. The therapy site was heated by infrared irradiation ofa transparent heating film. In this case, light penetrated through the film to obtaina therapeutic effect from light. Except for heat transfer analysis, details regardingthe development of therapeutic devices, including device components, have beendescribed previously [11, 12].

2. COMPUTATION

2.1. Computational Domain and Governing Equations

The computational domain was configured as shown in Figure 2, assumingthat the skin was heated by attaching a heating film with a radius of 2 cm. The depthof computation in the skin was chosen as 11.6 mm because heat must be able to reachthe muscle layer to obtain a therapeutic effect. As shown in the figure, the domainconsisted of a skin layer with a depth of 1.6 mm, a subcutaneous fat layer witha depth of 2.0 mm, and a muscle layer. In addition to the area for which heatingwas applied, a domain with radius of 4 cm was included to consider the coolingeffects mediated by surrounding air; this radius was determined through numericaltests to remove the effects of heating on the side edge.

The computational domain was assumed to be two-dimensional axisymmetric,and each layer had different thermophysical properties as shown in Table 1.

Figure 2. Computational domain for temperature analysis of skin layers.

TEMPERATURE AND BURN INJURY PREDICTION IN SKIN 923

Although the difference in physical properties among layers was not large, a previousstudy [13] suggested that the use of the same physical properties fails to show discon-tinuous changes in temperature between layers. Conversely, the physical propertieswere assumed to be constant in each layer with respect to temperature. The bloodperfusion rate was only considered in the muscle layer because it was very small inother layers. Air temperature, temperature of the bottom edge of the muscle layer(x¼ 11.6 mm), and convection heat transfer coefficient [9, 14] were 25�C, 37�C,and 10.0 W=m2 �K, respectively. Heating was carried out under constant heatflux or constant temperature. Adiabatic and symmetry conditions were applied tothe right and left boundaries of the computational domain. The initial temperatureprofile of the computational domain was identified by steady-state computation withthe boundary conditions described earlier.

We used the well-known Pennes bio-heat equation, which is a heat conductionequation for the computational domain that considers blood perfusion [3]. If T is thetemperature of a tissue, the equation can be expressed as

qcqT

qt¼ r � krT þ xbqbcbðTb � TÞ þ qm ð1Þ

where q, c, and k are the density, specific heat, and thermal conductivity,respectively, and the subscript b refers to the value of blood. In Eq. (1), xb and qm

represent the blood perfusion rate, which accounts for the amount of blood flowper unit volume of tissue and metabolic heat source. A metabolic heat source wasnot included in our computation due to its negligible order of magnitude comparedto other terms.

The degree of burns was predicted using the damage function X shown in thefollowing equation:

dXdt¼ A exp � DE

RT

� �ð2Þ

where A is a pre-exponential factor with a value of 1.3� 1095 1=s, DE is the activationenergy with a value of 6.04� 105 J=mol [14, 15], and R is the universal gas constant(8.3143 J=mol K). The damage function X can be calculated by integrating Eq. (2)over the time of heat exposure. The value of X defining burn injury severity differsslightly according to some previous studies [15–19]. In the present study, we definedfirst-degree burn as 0.53 and second-degree burn as 1.0 as described by Takada [18]and Ng and Chua [19].

Table 1. Thickness and material properties for human skin layers used in this study

Dermis Fat Muscle Blood

q (kg=m3) 1200 1000 1085 1060

c (kJ=kg �K) 3300 2674 3800 3770

k (W=m �K) 0.445 0.185 0.51 –

xb (1=s) – – 0.0027 –

Thickness(mm) 1.6 2.0 8.0 –

924 I.-T. IM ET AL.

2.2. Computation

A solution was found using numerical computations of the above equationwith the initial and boundary conditions described earlier. A first-order implicitmethod was used for finite differentiation for time and central differentiationfor space. A 300� 72 grid system was used after verifying grid-dependence ofthe solutions. In order to verify grid-dependence, steady-state computation wasperformed using three grid systems of 200� 48, 300� 72, and 300� 120. The resultfrom the densest 340� 120 grid system was almost identical to the result from the300� 72 grid system. For unsteady-state computations, the solution was computedup to 600.0 s using the variable size of time increment as 1.0–5.0 s.

The source term xbqbcb(Tb–T) in Eq. (1) was expressed in the form of AþBhusing enthalpy h during numerical computations [20]. In this case, A and B can bewritten as A¼ qbxbcbTb and B¼�qbxbcb=c.

3. RESULTS AND DISCUSSION

3.1. Verification of Computational Method

The exact solutions for the transient heat conduction problems in humanskin tissue were described previously by Deng and Liu [21]. Solutions from thecomputation were compared with the known exact solution in order to verifywhether the source term of the bio-heat equation given as Eq. (1) was consideredcorrectly in the numerical computations. Figure 3 shows the comparisons between

Figure 3. Comparisons of the transient temperatures obtained from the numerical method and

exact solutions.


the exact solutions and computational results with a one-dimensional problem withthe constant heat flux boundary condition considered by Deng and Liu [21]; thephysical properties of the skin tissue were the same as for their study. The two caseswith heat fluxes of 500 W=m2 and 1000 W=m2 were solved. The computationalsolutions were approximately the same as the exact solutions in both cases. Therefore,the numerical method used in this study was deemed appropriate.

3.2. Heating with Constant Heat Flux and Constant Temperature

Computations were carried out on two typical heating methods, one for whichconstant heat flux was applied to the heating film and the other for which a constantfilm temperature was maintained. First, we computed the case where the skin washeated on the heating part shown in Figure 2 at constant heat flux from 500 W=m2

to 3000 W=m2. Figures 4a and 4b show the changes in temperature on the skin surfaceand beginning part of the muscle layer according to time. Since the skin was heatedwith a constant heat flux, the temperature gradually increased with time. While thetemperature of the heated surface increased simultaneously with heating, the tempera-ture of the muscle layer was hardly changed during the early stage of heating, but it didincrease after reaching a specific time threshold. Although the temperature curvesexhibited a similar shape for the heat fluxes of 500 and 1000 W=m2, the temperaturedifference increased with time. Specifically, with a heat flux of 3000 W=m2, the tem-peratures of the skin and muscle layer rapidly increased during the early heating stage.

Figure 5 shows the temperature profiles at 300 s along the axis of symmetry ofthe center of the heat source in the direction of skin depth. The dotted lines referto the part where layers of skin tissue were changed. Temperature profiles showeddiscontinuous characteristics at the start of each layer. In particular, the slope ofthe temperature profile changed significantly at the start of the muscle layer.This was likely due to the large cooling effect induced by blood perfusion, whichwas taken into consideration for the muscle layer. With a heat flux of 700 W=m2,the surface temperature increased to 322 K.

Figure 6 shows the changes in damage functions with time according tovariation of heat flux. The skin did not suffer first-degree burn injury at 600 s whenheated at 500 W=m2, but did experience first-degree and second-degree burns at 424 sand 495 s, respectively, when heated at 700 W=m2. When heated at 1000 W=m2,first-degree and second-degree burns were observed at 218 and 242 s, respectively.Because the damage function is an exponential function that rapidly increases withincreasing temperature, it is necessary to maintain skin temperature lower thana specific threshold. The damage function had an extremely small value below10�3 during the early stage of heating when the temperature was lower than 320 K.

Figure 7 shows the computation results from heating at constant temperature,where Figure 7a shows the temperature variation of the muscle layer with time andFigure 7b shows the change in damage functions. When the skin was heated to 313,316, 318, 320, and 325 K, the temperature of the muscle layer increased to 311.3,312.6, 313.5, 314.4, and 316.7 K, respectively. According to the damage functionsof Figure 7b, skin burning did not occur until 600 s, at which time the temperatureof the heated region reached 320 K. However, first-degree and second-degree burnsdid occur at 57 s and 102 s, respectively, at a heating temperature of 325 K.

926 I.-T. IM ET AL.

3.3. Temperature Regulation using Heat Flux

As shown in Figure 7, the effects of heat treatment could be anticipated bymaintaining the desired temperature of skin tissue without burning the skin byheating at an appropriate constant temperature. However, it is difficult to maintain

Figure 4. Transient temperature profiles according to variations of heat flux: (a) skin temperature

and (b) muscle temperature.


a constant heating temperature in an actual therapy setting. A practical methodto maintain temperature within a narrow range is through repetition of heatingand cooling. On the other hand, as shown in Figures 4 and 6, continued heating

Figure 6. Damage functions with time according to variations of heat flux.

Figure 5. Temperature profiles at 300 s along the axis when heated by constant heat flux.

928 I.-T. IM ET AL.

with constant heat flux resulted in burning of the skin due to the increasedtemperature of skin tissue. Accordingly, the temperature of the heating region mustbe regulated to certain temperatures in actual therapeutic settings using repetitionof heating and cooling by applying heat flux in an on=off pattern as needed. In this

Figure 7. (a) Transient temperature variations of the muscle layer and (b) damage functions with respect

to time at a constant temperature condition.


case, it is necessary to determine the temperature for which heating and coolingoccur. In addition, energy consumption is dependent on heating time and heat flux.

In order to determine the appropriate periods of heating and cooling, we firstcalculated the process of heating to 320 K and cooling for 1 minute, the results ofwhich are shown in Figure 8. Heat flux was selected as 1000 W=m2 based on thecomputational results described earlier. In addition, the temperature at whichcooling initiated was set as 320 K based on the computation result above, such thatthe damage function yielded a very low value. A quasi-steady state was reached afterthe first two cycles, and the time taken to reach 320 K was fixed at 40 s. The damagefunction increased during heating and was maintained at a constant level whilecooling. However, due to the extremely minor incremental changes in the damagefunction, it was well-maintained below 0.05 after 600 s. Furthermore, the tempera-ture of the starting position of the muscle layer could be maintained at 312–313 Kby alternating heating and cooling after reaching the quasi-steady state.

Figure 9 shows the computation results for the case in which heat flux was2000 W=m2 and cooling by natural convection was applied when the temperaturereached 320 K; the cooling time was set to 60 s. A quasi-steady state was reachedafter three cycles, and time taken to reach 320 K was 25 s. The damage functionwas maintained at an extremely small value (approximately 10�2) because thetime taken to reach 320 K was shorter compared to the case with heat flux of1000 W=m2. However the temperature of the muscle layer was approximately313 K, which was almost identical to that in Figure 8, and had a heat flux of1000 W=m2. In addition, the total amount of heat supply up to 420 s was the same

Figure 8. Temperature and damage function variations according to the repetition of heating and cooling.

The heat flux given on the skin was 1000 W=m2, which was turned off when the skin temperature

reached 320 K.

930 I.-T. IM ET AL.



reached 320 K.



reached 325 K.


for the two cases at 240 kJ=m2. Therefore, the risk of burning could be reduced byheating for short periods of time at 2000 W=m2 compared to 1000 W=m2.

Figure 10 shows the results for the case in which heating was performedat 2000 W=m2 and stopped when the skin temperature reached 325 K, after whichcooling was allowed by natural convection. Since the damage function rapidlyincreases when the temperature exceeds 320 K, the damage function reached 0.5 after330 s, even when the skin was cooled after reaching 325 K. Thus, heating the skinto a temperature of 325 K is accompanied by a risk of burning.

4. CONCLUSIONS

In this study, the temperature profiles and degree of burns in human skin tissueafter heating at constant heat flux or constant temperature were predicted throughnumerical computation for the development of a combined therapy device usingheat and light. The exact solutions and numerical solutions for a one-dimensionalequation were compared to verify the validity of the computational method, andthe two solutions were in agreement with each other.

When a heat flux ranging from 500 to 3000 W=m2 was applied to the skin, thetemperatures of the skin and muscle layer increased with time, and temperatureincreased more rapidly at a higher heat flux. At a high heat flux, burn injuries canoccur during the early stages of the heating process. The temperature profiles inthe skin tissue layers exhibited different slopes at the boundaries between layersdue to the differences in physical properties among tissue layers and perfusion rateof the muscle layer. When the skin surface was maintained at a constant tempera-ture, there was no risk of burning up to 600 s when the skin temperature wasmaintained under 320 K. The damage function rapidly increased at 325 K, resultingin first-degree and second-degree burns at 57 s and 102 s, respectively. Thus, the riskof burning can be reduced by controlling the temperature of the skin below 320 Kthrough repeated on=off cycling of heat flux. Despite equivalent heat supply, the riskof burning was low when the skin was heated for a short time with 2000 W=m2

compared to a longer heating time with 1000 W=m2. This observation was attributedto the very low value of the damage function at 2000 W=m2 during short heating times.

FUNDING

This paper was supported by research funds of Chonbuk National Universityin 2012.

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Queima pele humana

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