ANALYZING EFFECT OF TEMPERATURE VARIATION ON SKIN SUB-LAYERS USING FINITE ELEMENT APPROACH

Transcription

1 Origin Reserch Artice Aied sciences Interntion Journ of Phrm nd Bio Sciences ISSN ANALYZING EFFECT OF TEMPERATURE VARIATION ON SKIN SUB-LAYERS USING FINITE ELEMENT APPROACH MONA DWIVEDI 1 * AND USHA CHOUHAN 1, Deprtment of Mthemtics, Mun Azd Ntion Institute of Technoogy, Bhop, M.P , Indi. ABSTRACT The temperture distribution in humn body regutes vriety of bioogic mechnism. Humn Skin is very compex structure nd bnormity in temperture of vrious yer of skin py importnt roe for curing nd tretment diseses ike tumor, cncer etc. The eight yers of humn skin nmey strtum corneum, strtum ucidum, strtum grnuosum, strtum spinosum, strtum germintivum, ppiry, reticur nd subcutneous tissue re considered for the study. A one dimension Finite eement mode is deveoped to study the temperture distribution invoving bood circution rte, metboic het genertion nd therm conductivity in humn skin. A MATLAB progrm hs been deveoped to obtin the numeric resuts. KEYWORDS: Temperture Distribution, Bood mss fow rte, Derm yers, Finite Eement Method, Therm Conductivity MONA DWIVEDI* Deprtment of Mthemtics, Mun Azd Ntion Institute of Technoogy, Bhop, M.P , Indi. Received on: Revised nd Accepted on: DOI: B-675

2 INTRODUCTION The humn thermoregutory is very compex system nd it incudes more contro processes thn ny technic contro system. 1 Humn skin is very compex tissue consisting of sever distinct yers nd components. Humn body mintins its body core temperture constnt within sm rnge between (37±0.6) C. Skin temperture distribution of the humn body is compex interction of physic het exchnge processes nd the potenti for physioogic djustment. Temperture infuences the functioning of bioogic systems. The SST region consist miny three yers nmey epidermis, dermis nd subcutneous tissue. Epidermis is the most outer yer. The outer most yer divided in to five yers nmey strtum corneum, strtum ucidum, strtum grnuosum, strtum spinosum nd strtum (bse) germintivum. The temperture regution in humn body is ccompished through sever mjor mechnisms. These re bood fow, temperture of incoming rteri bood, nd het exchnge with the environment. 3 The skin surfce is ssumed to expose to the environment nd the outer skin surfce temperture is considered to be equ to the tmospheric temperture.the chnge in the temperture of the surroundings so ffects the temperture of the humn skin. The skin temperture is the cruci temperture when we refer to the skin s biity to ose het to the surrounding mbience. 4 Humn body perpetutes its body core temperture t uniform temperture under the norm tmospheric conditions. In order to mintin this core temperture, prmeters ike rte of bood mss fow, rte of metboic het genertion nd therm conductivity differ in response to chnges in surrounding conditions. 5 However, in extreme prts of humn body the core temperture is not uniform t ow tmospheric temperture. This my be becuse the rteri bood hs cooed down whie trveing towrds the extremities. The het fow in in-vivo tissues given by temperture distribution in tissue medium. 6 Ptterson 7 mde n ttempt for experiment determintion of temperture probems in Skin nd Subcutneous Tissues (SST) region. Sxen nd Ary 8 deveoped three yered finite eement mode to find the temperture probems in SST region for one dimension stedy stte cse. Cooper nd Trezek 9 found n nytic soution of het diffusion eqution for brin tissue with negigibe effect of bood fow nd metboic het genertion. Trezek nd cooper 10 computed the therm conductivity of the brin tissue by considering the prmeters s constnts. Sever computer-simuted modes of temperture distribution in humn derm system hve been deveoped. The im of our study is to deveop mode describing temperture distribution in humn derm prts nd to ccute the temperture distribution t muti-yered skin nd sub-derm tissues by using vrition finite eement method. The present work is n ttempt to study the distribution of temperture t deep derm yers for heterogeneous therm conductivity s function of temperture. Figure 1 Humn Skin yer 11 The Penne s mode is used to ddress the het exchnge in iving tissues. This mode is bsed on the ssumption of the energy exchnge between the bood vesses nd the surrounding tissues. Penne s mode my give suitbe temperture distributions in whoe body, orgns nd tumor nysis. 1 This formution wi now be extended to incorporte het sources nd boundry conditions tht cn vry with time. Mny interesting bio-het ppictions invove heting nd cooing by time-vrying environment or therpeutic infuences. 13 Het trnsfer probems in humn re reted to medic sciences nd hve roe in tretment nd in the dignosis of deceses ike tumor, skin burn, skin itching etc. They cn estimte the time nd the course of tretment with informtion on the temperture where thermometry is cking. Het trnsfer in bioogic system invoves metboic het genertion, conduction, convection, rdition, evportion nd bood perfusion in humn tissue but physioogic function genertes het by mens of metboic rection in bioogic systems. 14 The bnce between the het genertion nd oss from the body to the environment is very importnt to mintin body core temperture. Any physioogic bnormity wi disturb the homeosttic conditions for the temperture. 15 Therefore the study of het trnsfer under norm nd bnorm conditions wi be usefu for vrious cinic conditions. The go of our study is to deveop mode describing temperture in humn derm prts. B-676

3 MATHEMATICAL MODEL The Mthemtic mode used for bio-het trnsfer is bsed on the penne eqution 11 which incorporte the effect of metboism nd bood perfusion in to the stndrd therm diffusion eqution: T ρc = Κ T + cmw b b b( T T) + S (1) t x x Here ρ, x, c, K nd S re respectivey the density, specific het, therm conductivity nd rte of metboic het genertion in tissues. Aso the other quntity w b, m b, c b nd T re the bood perfusion rte, the bood mss fow rte, specific het of the bood, nd rteri bood temperture respectivey. Figure Finite Eement Discretiztion of Eight yers of Skin with Nine Nod Points The oss of het from the skin surfce due to convection, rdition nd evportion is considered. So the mixed boundry condition is tken s: Where, h=combined het trnsfer coefficient due to convection nd rdition T =Surrounding temperture, L=Ltent het of evportion, E=Rte of swet evportion, the inner body core temperture T b is ssumed to be 37 C. The thickness of strtum corneum, strtum ucidum, strtum grnuosum, strtum spinosum, strtum germintivum (bse), ppiry region, reticur region nd subcutneous tissue hve been considered s 1, 1, 3, T K = h( T T ) + LE () t At skin outer surfce,,,, respectivey nd T 0, Tbe 1 Shpe function t different yers of skin T 1, T, T 3, T 4, T 5, T 6, T 7 nd T 8 = T b re the nod tempertures t distnces x= 0, x= 1, x=, x= 3, () i x= 4, x= 5, x= 6, x= 7 nd x= 8. T (i = 1,, 3, 4, 5, 6, 7, 8) be the temperture functions in the yers strtum corneum, strtum ucidum, strtum grnuosum, strtum spinosum, strtum germintivum (bse), ppiry region, reticur region nd subcutneous tissue respectivey. B-677

4 Vues of T (i) Tbe, K (i) (i), M (i) = w (i) b * m (i) b *c (i) b nd S (i) t i th eement of skin yers th i Eement Nme of the yer 1 Strtum Corneum Strtum ucidum 3 Strtum gruosum 4 Strtum Spinosum 5 Strtum Germintivum 6 Ppiry Region 7 Reticur Region 8 Subcutneous Tissue ( i) T (1) () T = T b T = T b T = T b ( i) K (1) K = () K = K = K = K = K = K = K = ( i) M (1) M = () M = M = M =174 M =61 M = M =198.1 M =198.1 ( i) S (1) S = () S = S = S = S = S = S =156 S =156 SOLUTION OF PROBLEM The vrition integr form of (1) in one dimension unstedy stte cse together with outer skin boundry condition () is given by 1 1 T T 1 I = K M( T ) ( ) 0 + T ST+ ρc dx+ h T T + LET x t where, M=w b *m b *c b We ccute I seprtey for the eight eements of skin yers: I 1 for strtum corneum, I for Strtum ucidum, I 3 for Strtum gruosum, I 4 for Strtum spinosum, I 5 for Strtum Germintivum, I 6 for ppiry region, I 7 for reticur region nd I 8 for subcutneous tissue. 1 1 I = K + M T T S T + c dx+ h T T + LET dx ( 1) ( 1) 1 ( 1) ( 1) ( 1) ( 1) ( 1) ( 1) T ( ) ( ) 0 ρ ( ) ( ) 1 ( ) ( ) ( ) ( ) ( ) ( ) ( ) T I = K M T T S T ρc dx 1 dx ( 3) ( 3) 1 ( ) ( ) ( ) ( ) ( ) ( ) ( ) T I3 = K M T T S T ρc dx dx ( 4) ( 4) 1 ( ) ( ) ( ) ( ) ( ) ( ) ( ) T I4 = K M T T S T ρc dx 3 dx ( 5) ( 5) 1 ( ) ( ) ( ) ( ) ( ) ( ) ( ) T I5 = K M T T S T ρc dx 4 dx ( 6) ( 6) 1 ( ) ( ) ( ) ( ) ( ) ( ) ( ) T I6 = K M T T S T ρc dx 5 dx ( 7) ( 7) 1 ( ) ( ) ( ) ( ) ( ) ( ) ( ) T I7 = K M T T S T ρc dx 6 dx (9) (10) B-678

5 ( 8) ( 8) 1 ( ) ( ) ( ) ( ) ( ) ( ) ( ) T I8 = K M T T S T ρc dx 7 dx (11) Evuting the integr I i (i=1,, 3,...8) with the hep of yers wise ssumptions. Now the integrtes Iire evuted from the eqution to (11) re ssembed s: I 8 = Ii (1) i= 1 we substitute T8= Tbin bove eqution (1),where Tb is the body core temperture. Now I is extremized with respect to nod temperture T0, T1, T, T3, T4, T5, T6, T 7 s given beow: 8 di dii = = 0, j= 0,1,,...7 (13) dt dt j i= 1 j We get system of ordinry differenti eqution is mtrix form s: T C + PT = W t Where, T0 t T1 t T0 T T 1 t T T 3 T3 T t T = nd = T4 t T4 T t 5 T T 6 5 T t 7 T6 t T7 t (14) (15) C nd Pre system mtrices nd W is system vector. To sove the system of ordinry differentition eqution (14) we use Crnk-Nicoson method. This method moves the soution of the system hed in time ccording to the retion 16 t ( i+ 1) t ( i) C+ PT = C PT + tw (16) (0) where tis step size of time, nd T is 8 1mtrix for initi nod tempertures t time t=0sec. Genery, under norm condition the temperture decreses from body core towrds skin surfce. Hence we considert 0, T 1, T, T 3, T 4, (0) T 5, T 6, T 7 nd T 8 in iner order towrds body core t t=0. Thus we ssume the foowing initi condition for T (,0) ( 0,0) T x = T + rx (17) Considering initi temperture 3 C t skin surfce becuse t norm tmospheric tempertures skin surfce temperture is round 3 C nd r is constnt. B-679

6 NUMERICAL RESULTS AND DISCUSSION The foowing vues of physic nd physioogic prmeters hve been used s prescribed 1, 4, 5, 9, 11 to compute the numeric resuts. They re tbuted in Tbes 1,, 3 nd 4. Tbe 3 Vue of Biophysic Prmeters N Prmeter Vue Unit L J/kg h 6.80 w/m C c J/kg C ρ Kg/m E w/m Tbe 4 Two Sets of Derm Lyers Sets 0 (m) 1 (m) 3 4 (m) I II The Pennes biohet eqution determining the temperture in the muti-yer humn skin hs been modeed by Finite eement method. The physic region is being discretized into mny sm sub regions nd the vue of vrious physioogic quntities t every grid point is suppied for ech time step. The vrition integrs corresponding to ech of the sub regions were ccuted to estimte the temperture t ech yer. The numeric vue of temperture t ech nod points obtined from eqution (16) is shown in figures beow by tking vrious tmospheric tempertures. The unstedy stte temperture profies re presented in figure 3 to figure 6 for the two set of skin thickness t different tmospheric tempertures. We observed from these figures tht the curves for the nod temperture rises more rpidy in set I nd rech stedy stte cse erier s compre to set II dt of thickness. This is hppen due to ower thickness of skin in dt set I thn to dt set II. We so observed tht the temperture f down s we move wy from body core to the skin surfce. The tempertures T i re hving higher vues t high tmospheric tempertures s compred to ow tmospheric tempertures. But the difference between initi temperture nd the temperture t time t=10000sec is higher for the ow tmospheric temperture s compred to high tmospheric tempertures. This is becuse more het moves outsides by swet evportion t higher tmospheric tempertures. The thicknesses of the skin nd vrious tmospheric conditions hve the significnt effects on the temperture of skin yers. () (b) Figure 3 Tempor temperture vrition t tmospheric temperture 15 C on different nod points for () SET I (b) SET II B-680

7 () (b) Figure 4 Tempor Temperture Vrition t tmospheric temperture 0 C on different nod points for () SET I (b) SET II () (b) Figure 5 Tempor Temperture Vrition t tmospheric temperture 85 C on different nod points for () SET I (b) SET II () (b) Figure 6 Tempor Temperture Vrition t tmospheric temperture 90 C on different nod points for () SET I (b) SET II B-681

8 CONCLUSION The present study provides n insight on temperture distribution in humn skin ffected by mbient temperture. The mode cn be used for predicting skin temperture response in extreme cod nd extreme hot conditions. The one dimension unstedy stte finite eement mode seems more reistic. Though there re so mny yers in the humn skin, we hve tken ony eight yers of derm prts: strtum corneum, strtum ucidum, strtum gruosum, strtum spinosum, strtum germintivum, ppiry region nd reticur region nd subcutneous tissue. The theoretic resuts obtined here for temperture profie of skin under different mbient conditions re in good greement with the bioogic nd physic fcts. These resuts my be usefu for biomedic scientists nd physioogists to detect the vrious bnormities occur in humn skin due to het fow. CONFLICT OF INTEREST Confict of interest decred none. REFERENCES 1. Achry S, Gurung DB nd Sxen VP, Effect of Metboic Rections on Thermoregution in Humn Mes nd Femes Body. Appied Mthemtics. 013; 4: Achry S, Gurung DB nd Sxen VP, Time Dependent Temperture Distribution Mode in Lyered Humn Derm Prt. Kthmndu University Journ of Science. 01; 8: Agrw M, Adkh N, nd Prdsni KP, Therm Disturbnces in Derm Regions of Humn Limbs Invoving Metstsis of Tumors. Interntion Mthemtics Forum. 010; 5(39): Guyton AC, H JE. Textbook of Medic Physioogy.11th edition. 006; Gurung DB, Thermoregution Thorough Skin t Low Atmospheric Tempertures. Kthmndu University Journ of Science. 008; 5: Per W, Het nd mtter distribution in body tissues nd determintion of tissue bood fow by oc cernce methods. Journ of Theoretic Bioogy. 196; : Ptterson AM, Mesurement of temperture profies in humn skin. South Africnn Journ of Science. 1976; 7: Sxen VP, nd Ary D, Stedy stte het distribution in epidermis, dermis nd subderm tissues, Journ of Theoretic Bioogy. 1981; 89: Cooper TE, nd Trezek GJ, A probe technique for derterminig the therm conductivity of tissue. Journ of Het Trnsfer ASME, 197; Trezek GJ, nd Cooper TE, Anytic determintion of cyindric source temperture fieds nd their retion to therm diffusivity of brin tissues. Therm Probems in Biotechnoogy. ASME N.Y, 1968; Bhrgv T, Rmchndni U, Shrivstv SK, nd Dubey PK, Current trends in NDDS with speci reference to NSAIDS. Interntion Journ of Phrm nd Bio Sciences. 011; : Pennes HH, Anysis of tissue nd rteri bood tempertures in resting humn forerm. Journ of Appied Physioogy. 1984;1:93 1, 13. Durkee Jr JW, nd Antich PP, Exct soutions to the muti-region time-dependent biohet eqution with trnsient het sources nd boundry conditions. Physics in Medicine nd Bioogy-IOP science.1991; 36: Shen W, nd Zhng J, Modeing nd Numeric Simution of Biohet Trnsfer nd Biomechnics in Soft Tissue. Mthemtic nd Computer Modeing. 005; 41: Gurung DB, Two dimension temperture distribution mode in humn derm region exposed t ow mbient temperture with ir fow, Kthmndu university Journ of Science Engineering nd Technoogy. 01; 8(11): Kwon YW, Bng H. The finite eement method using MATLAB. CRC press; 000. B-68