Bio-Heat-Transfer Equation (BHTE) Analysis in. Cancer Cell Using Hyperthermia Therapy Case. Study in Ambon Moluccas Indonesia

Transcription

1 Applied Mahemaical Sciences, Vol. 12, 2018, no., HIKARI Ld, hps://doi.org/ /ams Bio-Hea-Transfer Equaion (BHTE Analysis in Cancer Cell Using Hyperhermia Therapy Case Sudy in Ambon Moluccas Indonesia Alwi Smih Biological Educaion Deparmen, Educaion Faculy Paimura Universiy, Moluccas, Indonesia Address: Ir. M. Puuhena Sree Poka, 97233, Moluccas, Indonesia Copyrigh 2018 Alwi Smih. This aricle is disribued under he Creaive Commons Aribuion License, which permis unresriced use, disribuion, and reproducion in any medium, provided he original work is properly cied. Absrac Hyperhermia is one of he mehod in medical reamen simulaion o overcome he cancer disease. In hyperhermia, i is used he elecromagneic wave as hea source in human body hea ransfer. This hea ransfer is mahemaically simulaed by Bio-Hea-Tranfer-Equaion (BHTE. In his research, he boundary hea reshold in muscle, fa and umor relaed o hyperhermia herapy is being prediced. Keywords: Cancer, Hyperhermia, boundary hea reshold, Bio-Hea-Transfer- Equaion Inroducion Cancer is one of he common erminology o express he malignan neoplasma [1]. Lierally, neoplasma means new growh. ills said ha cancer is abnormal mass in issue which is unconrollably grown so ha disurb he normal issue growh [].

2 176 Alwi Smih Cancer is one of he deah main cause in developmen counry. In Unied Saes and anoher several developmen counry, hey have 25% of cancer deah. During a year, i is abou 0,5% of heir populaion diagnosed have a cancer [2]. This condiion is no he same one as in Moluccas. According o Malukunews.com newspaper in 25 Juni 2015, in Indonesia, especially in Moluccas, he local governmen has held a lo of effors in cancer handling program. Moluccas local healh deparmen has held he papsmer check up and examinaion on 00 ciizens of Ambon. According o is resul, here is no ciizen inveced by cancer. Local governmen of Ambon ogeher wih he Singapore naional cancer cenre docor eam, give socializaion relaed o he head, neck and breas cancer o he 200 of womens. Furhermore, hese womens can also closely consul abou heir healh o hem. All of hese effor is purposed o obsruc he growh of cancer sufferer in Ambon, Moluccas. Hyperhermia is one of he mehod in medical reamen simulaion o overcome he cancer disease. Hyperhermia use he elecromagneic wave as hea source o ransfer he hea in human body. This hea ransfer is simulaed by Bio- Hea-Tranfer-Equaion (BHTE mahemaically. In his research, he boundary hea reshold in muscle, fa and umor relaed o hyperhermia herapy is being prediced. Bio-Hea-Transfer Equaion (BHTE Bio-he-ransfer-equaion (BHTE is an equaion in medical planning in hyperhermia reamen simulaion. In hyperhemrnia medical reamen use he elecromagneic wave which play roles as hea source o ransfer he hea in human body. The bio-hea-ransfer-equaion is given as follow: T c k T C T T ARD b b where represen he densiy of issue, c is a cerain hea, k is he hermal conduciviy, represens he blood perfussion, T is emperaure, and ARD is he period source. This equaion means ha he blood perfussion ( use he non linear version o fa perfusion which relaed o he muscle. This blood perfussion is no depended o he emperaure. However, several experimen shows ha blood vessels in issue o ge he hea ino cancer is depends o he emperaure. If he hea is given o he normal issue, such as skin and muscle, hen he hea will increase significanly. So, he blood perfussion and normal issue in muscle, fa and umor combinaion is needed o have he nonlinear version of

3 Bio-hea-ransfer equaion (BHTE analysis in cancer cell 177 equaion. According o his condiion, his model depends on he blood hea perfussion and umor. So, we ge he following blood perfussion in muscle, fa and umor [3]: muscle,0 1,0723( T 5 (1 fa 0,72 0,0682( T 5 (2 umor 0,833 0,68( T 5 (3 Resul and Discussion In bio-hea-ransfer-equaion relaed o he hyperhermia herapy, each variable is influenced one anoher wihin he emperaure (T. The daa of he paien condiion can be seen in Table 1. Table 1. Clinical Pahalogy and Analomy Resul No Paien Iniial M/F Age Hb Leuco Led Tromb D.L D.T D.O 1 ARB M 50 75, ,720-2 AUM F , , RLO M , STA F , YRI M , ,650 (Source: Ambon Dr.M Haulussy Hospial, 2016 Le T 0 0 so f ( T 0 and T 1 5 so f ( T 0. According o Table 1, we found ha muscle muscle 0,650. So, from Equaion (1 we ge ha:,0 1,0723( T 5 0,650,0 1,0723( T 5 Le Y 0 f ( T 0, Y f ( 1 1 T and Y f ( T, so we ge: 6,0 0,650 1,0723(0 5, Y0 10

4 178 Alwi Smih Y 1 3,35 1,0723(5 5 3,35 From he equaions above, we ge he nonlinear equaion of bio-he-ransfer of blood perfussion. The firs sep is o find he iniial poin of is soluion using Table 2. From Table 2, we can see ha for he inerval T [3,] is where he soluion placed. Table 2. Ieraion of iniial poins of Ieraion T Y f T muscle soluion ( 1 0 -, E , E , E , E , E , E , E , E , E+00 So, we can ge he soluion wih is error olerance is e as he following Table 3. In able 3 shows ha he emperaure soluion of muscle is 3,701 F wih is eror is 0, So, for paien wih iniial name YRI besly have he 3,701 F emperaure relaed o he muscle hyperhermia herapy. Table 3. The soluion of muscle equaion wih is error Ieraion T Y T-new error , ,1777 3,865 0, ,865 1,680 3,586 0, ,586-1,05 3,701 0, ,701 0,2025 0,

5 Bio-hea-ransfer equaion (BHTE analysis in cancer cell 179 Le T 0 0 so f ( T 0 and T 1 5 so f ( T 0. According o Table 1, we found ha fa 0,05. So, from Equaion (2 we ge ha: fa 0,72 0,0682( T 5 0,05 0,72 0,0682( T 5 Le Y 0 f ( T 0, Y f ( 1 1 T and Y f ( T, so we ge: 5 0,72 0,05 0,0682(0 5 2, Y0 10 Y1 0, 67 0, 0682( 5 5 0, 67 The iniial poin of Table below. fa nonlinear equaion soluion can be seleced from Table. Ieraion of iniial poins of fa soluion Ieraion T Y f T 1 0-2, E , E , E , E , E , E , E , E+01 ( From Table, we can see ha he emperaure soluion is in he inerval T [0,] fa. Then, we can see he soluion of emperaure in nonlinear equaion as described in Table 5. In Table 5 we ge ha he emperaure soluion fa of is 3,356 F wih is eror is 0, So, for paien wih iniial name AUM have he 3,356 F of emperaure reshold relaed o he fa hyperhermia herapy.

6 180 Alwi Smih Table 5. The soluion of fa equaion wih is error Ieraion T Y T-new error , ,3800 3, ,957 56,7827 2, , , ,723,1026 3, ,56 30,367 3, ,212-21,029 3, ,356 0, Le T 0 0 so f ( T 0 and T 1 5 so f ( T 0. According o Table 1, we found ha umor 0,720. So, from Equaion (3 we ge ha: umor 0,833 0,68( T 5 0,72 0,833 0,68( T 5 Le Y 0 f ( T 0, Y f ( 1 1 T and Y f ( T, so we ge: 6 0,833 0,72 0,68(0 5 1, Y0 10 Y1 0113, 0, 68( , The iniial poin of umor nonlinear equaion soluion can be seen from Table 6. Table 6. Ieraion of iniial poins of umor soluion Ieraion T Y f T ( 0 0-1, E , E , E , E , E+06

7 Bio-hea-ransfer equaion (BHTE analysis in cancer cell 181 Table 6. (Coninued: Ieraion of iniial poins of umor soluion 5 1-1, E , E , E , E , E-01 From Table 6, we can see ha he inerval T [0,] included he umor emperaure soluion of soluion of emperaure in umor nonlinear equaion. Furhermore, we can see he nonlinear equaion as described in Table 7. Table 7. The soluion of umor equaion wih is error Ieraion T Y T-new error 1-0, ,1130, ,759 0,111 27, , ,0219, ,759 0,111, E-06 6,758 0,111 0, ,53-185,9993, ,756 0,1113, E-05 9,753 0,1113 0, , ,703, ,751 0,1112, E-05 12,78 0,1111 0, , ,8298, ,7 0,1110, E-05 15,71 0,1109 1, ,272-90,266,

8 182 Alwi Smih Table 7. (Coninued: The soluion of umor equaion wih is error 17,737 0,1107, E-05 18,732 0,1106 1, ,580-63,910, ,727 0, umor In Table 7 we ge ha he emperaure soluion of is,727 F wih is eror is 0, So, for paien wih iniial name ARB have he,727 F of emperaure reshold relaed o he umor hyperhermia herapy. Conclusion From his research, i is shown ha he reshold emperaure soluion relaed o hyperhermia herapy is deermined differenly in each paien. I is depend on heir blood perfussion in each organ. For he paien wih iniial YRI besly have he 3,701 F emperaure relaed o he muscle hyperhermia herapy, for paien wih iniial name AUM have he 3,356 F of emperaure reshold relaed o he fa hyperhermia herapy and for paien wih iniial name ARB have he,727 F of emperaure reshold relaed o he umor hyperhermia herapy. References [1] F. Macdonald, C.H.J. Ford, Elizabeh Hospial, A.G. Casson, Molecular Biology of Cancer, Second Ediion, Garland Science/BIOS Scienific Publishers, London, [2] HO and Naional Cancer Insiue (NCI, 201. Cancer Moraliy and Morbidiy, Accesed in 21s of March hp:// [3] Bodo Erdmann, Jens Lang and Marin Seebab, Adapive Soluions of Nonlinear Parabolic Equaions wih Applicaion o Hyperhermia Treamens, Proceedings of he Inernaional Symposium on Advances in Compuaional Hea Transfer, Berlin Dahlem, hps://doi.org/ /ichm.1997.insymliqwophaseflowranspphench.90

9 Bio-hea-ransfer equaion (BHTE analysis in cancer cell 183 [] Lumungga, Dukungan Sosial Pada Pasien Kanker, USU Press, Medan. Indonesia, Received: January 12, 2018; Published: February 8, 2018