n this paper, the relationship between electromagnetic power absorption and temperature distributions inside highly heterogeneous biological samples was accurately determinated using finite volume method. An in-vitro study on pineal gland that is responsible for physiological activities was for the first time simulated to illustrate effectiveness of the proposed method

Cai, Zhaoquan

Cen, Wei

Gu, Ning

Hoppe, Ralph

Lu, Rongbo

AIP Advances

In this paper, the relationship between electromagnetic power absorption and temperature distributions inside highly heterogeneous biological samples was accurately determinated using finite volume method. An in-vitro study on pineal gland that is responsible for physiological activities was for the first time simulated to illustrate effectiveness of the proposed method

Wei Cen

Ralph Hoppe

Rongbo Lu

Zhaoquan Cai

Ning Gu

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3D highly heterogeneous thermal model of pineal gland in-vitro study for electromagnetic exposure using finite volume method

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TU Ilmenau | Universitätsbibliothek | ilmedia, 2019 http://www.tu-ilmenau.de/ilmedia Cen, Wei; Hoppe, Ralph; Lu, Rongbo; Cai, Zhaoquan; Gu, Ning: 3D highly heterogeneous thermal model of pineal gland in-vitro study for electromagnetic exposure using finite volume method Original published in: AIP Advances. - New York, NY : American Inst. of Physics. - 7 (2017), 8, art. 085222, 9 pp. Original published: 2017-08-25 ISSN: 2158-3226 DOI: 10.1063/1.4991464 [Visited: 2019-04-10] This work is licensed under a Creative Commons Attribution 4.0 International license. To view a copy of this license, visit  http://creativecommons.org/licenses/by/4.0/ AIP ADVANCES 7, 085222 (2017)3D highly heterogeneous thermal model of pineal glandin-vitro study for electromagnetic exposure using finitevolume methodWei Cen,1,2 Ralph Hoppe,3 Rongbo Lu,4 Zhaoquan Cai,5,band Ning Gu6,a1Technische Universita¨t Ilmenau, 98684, Germany2Nanjing University of Chinese Medicine, 210023, China3Ganzheitliches Gesundheits Zentrum, 34305, Germany4Jishou University, 416000, China5Huizhou University, 516007, China6The Third Affiliated Hospital of Nanjing University of Chinese Medicine, 210001, China(Received 21 June 2017; accepted 7 August 2017; published online 25 August 2017)In this paper, the relationship between electromagnetic power absorption and tempera-ture distributions inside highly heterogeneous biological samples was accurately deter-minated using finite volume method. An in-vitro study on pineal gland that is responsi-ble for physiological activities was for the first time simulated to illustrate effectivenessof the proposed method. © 2017 Author(s). All article content, except where oth-erwise noted, is licensed under a Creative Commons Attribution (CC BY) license(http://creativecommons.org/licenses/by/4.0/). [http://dx.doi.org/10.1063/1.4991464]I. INTRODUCTIONIn recent years, wireless telephones have been widely used in our life. There is an increasing publicconcern about the health hazards resulting from exposure to cell phone radiofrequency (RF) radiation.The International Agency for Research on Cancer (IARC) classified RF radiation as a possible humancarcinogen.1 An interesting finding of the U.S. National Toxicology Program (NTP) support theIARC conclusions regarding the possible carcinogenic potential of RF radiation and reports that“low incidences of tumors in the brains and hearts of male rats, but not in female rats.”2 Temperatureelevation from RF energy absorption (usually expressed in terms of the specific absorption rate SAR)is known to be a dominant factor inducing adverse health effects. The difficulty existing in the analysisof the temperature rise in biological bodies caused by electromagnetic fields is the highly complexcomputation and the lack of preciseness.The bio-heat transfer equation for homogeneous material model can be easily calculated by usingsecond order finite difference approximation to discretize the spatial derivatives. However, for highlyheterogeneous thermal model, the spatial derivative∇(K ·∇T ) is difficult to be discretized using FDTD.For a large object, such as human head or human body, the second order finite difference expressionsmight be suitable enough, but in practice, the in-vitro studies on cells or isolated tiny tissues are oftendesirable which require accurate simulation. To overcome the disadvantages of the FDTD method, theFinite Volume Method (FVM)3 has been investigated by researchers. The method is based on integralconservation and therefore has distinct advantages for being readily applicable to multidimensionalproblems involving variable mesh and physical properties. We propose numerical methods that useFVM method to analyse the fundamental problem of bio-heat transfer caused by electromagnetic(EM) exposure for inhomogeneous materials models. To the best of our knowledge, the methodhas not been utilized to calculate bio-thermal response of pineal gland caused by electromagneticexposure. Melatonin which is secreted by the pineal gland in the brain is a major regulator of coreaCorresponding author: sonnelichtsonne@gmail.combCorresponding author: caizhaoquanhz@163.com2158-3226/2017/7(8)/085222/9 7, 085222-1 © Author(s) 2017      085222-2 Cen et al. AIP Advances 7, 085222 (2017)body temperature. We recently conducted an in-vitro study on pineal gland that is responsible forphysiological activities.II. METHODSBiological media are highly heterogeneous, thermal conductivity K varies from tissue to tissue.The bio-heat transfer equation is expressed as:4∇(K · ∇T ) + A0 + SAR · ρ − B · (T − Tb)=Cp · ρ · ∂T∂t(1)with the boundary conditionK∂T∂n=−h · (T − Ta) (2)where K is the thermal conductivity [J/(s ·m · ◦C)]; A0 is volumetric heat sources [J/(s ·m3)] dueto metabolic processes; the specific absorption rate (SAR) is the input EM heating source intothe bio-heat equation; B is a parameter proportional to the blood perfusion [J/(s ·m3 · ◦C)]; Taisthe ambient temperature; Tb is the blood temperature; h is the convective heat-transfer coeffi-cient [W /m2 · ◦C]; and Cp [J/(kg · ◦C)] and ρ [kg/m3] are the tissue specific heat and density,respectively.Many tasks require the in-vitro studies on cells or isolated tiny tissues. If the solution is notsufficiently smooth, the order of accuracy will be reduced. This can happen if the coefficients arenot smooth, e.g., due to the thermal conductivity jump across the interface of different tissues. Wepropose in this context the FVM method which is fully compatible with the FDTD method and allowsthe use of highly inhomogeneous objects. FVM is developed from integral interpolation method ofFD. As the name implies, a finite-volume formulation involves integrating equation over a controlvolume (CV).The method has been described previously.5 Briefly, using the notations in field theory, Eq. (1)can be rewritten as:∂T∂t= div(ν · gradT ) + S (3)where ν = KCp ·ρ , S =A0+SAR ·ρ−B ·(T−Tb)Cp ·ρ .Integrating Eq. (3) in the control unit [xi−1/2, xi+1/2] × [yj−1/2, yj+1/2] × [zk−1/2, zk+1/2] × [tn, tn+1]for each CV:$Vtn+1∫tn∂T∂tdtdxdydz=tn+1∫tn$Vdiv(νgradT )dxdydzdt +tn+1∫tn$VSdxdydzdt (4)The integral on the left-hand side of Eq. (4) can be removed by means of the mean value theoremfor integrals. Similarly, the integral over S is removed. The volume integral over the divergenceof the heat flux vector is transformed to a surface integral by means of the divergence theorem∫V∇·(νgradT )dV =∫S(νgradT ) · ~ndS =∫Sν ∂T∂n dS. Eq. (4) can be expressed as:∆xi−1 + ∆xi2· ∆yj−1 + ∆yj2· ∆zk−1 + ∆zk2· (Tn+1ijk − Tnijk)=∆yj−1 + ∆yj2· ∆zk−1 + ∆zk2·∫ tn+1tn[(ν dTdx )i+ 12 ,j,k− (ν dTdx )i− 12 ,j,k]dt+∆xi−1 + ∆xi2· ∆zk−1 + ∆zk2·∫ tn+1tn(ν dTdy )i,j+ 12 ,k − (ν dTdy )i,j− 12 ,kdt+∆xi−1 + ∆xi2· ∆yj−1 + ∆yj2·∫ tn+1tn[(ν dTdz )i,j,k+ 12− (ν dTdz )i,j,k− 12]dt+∆xi−1 + ∆xi2· ∆yj−1 + ∆yj2· ∆zk−1 + ∆zk2·∫ tn+1tn¯Si,j,kdt(5)085222-3 Cen et al. AIP Advances 7, 085222 (2017)Using half-grid central differences, Eq. (5) can be simplified to yield Temperature updating equation:Tn+1ijk =Tnijk +2 · ∆t · νi− 12 ,j,k(∆xi−1 + ∆xi) · ∆xi−1 Tni−1,j,k +2 · ∆t · νi+ 12 ,j,k(∆xi−1 + ∆xi) · ∆xi Tni+1,j,k−(2 · ∆t · νi− 12 ,j,k(∆xi−1 + ∆xi) · ∆xi−1 +2 · ∆t · νi+ 12 ,j,k(∆xi−1 + ∆xi) · ∆xi )Tni,j,k+2 · ∆t · νi,j− 12 ,k(∆yj−1 + ∆yj) · ∆yj−1 Tni,j−1,k +2 · ∆t · νi,j+ 12 ,k(∆yj−1 + ∆yj) · ∆yj Tni,j+1,k−(2 · ∆t · νi,j− 12 ,k(∆yj−1 + ∆yj) · ∆yj−1 +2 · ∆t · νi,j+ 12 ,k(∆yj−1 + ∆yj) · ∆yj )Tni,j,k+2 · ∆t · νi,j,k− 12(∆zk−1 + ∆zk) · ∆zk−1 Tni,j,k−1 +2 · ∆t · νi,j,k+ 12(∆zk−1 + ∆zk) · ∆zk Tni,j,k+1−(2 · ∆t · νi,j,k− 12(∆zk−1 + ∆zk) · ∆zk−1 +2 · ∆t · νi,j,k+ 12(∆zk−1 + ∆zk) · ∆zk )Tni,j,k + ∆t · ¯Si,j,k(6)In order to ensure the numerical stability, the maximum time step is chosen to satisfy the stabilitycriterion δt ≤ 2ρcpδmin212k+Bδmin2which was derived from Von Neumann’s condition.6By expanding in its finite volume approximation, Eq. (2) can be written asTn+1imin ,j,k =2Kimin ,j,k · Timin+1,j,k − hTa(∆ximin+1 + ∆ximin )2Kimin ,j,k − h · (∆ximin+1 + ∆ximin )(7)FIG. 1. Central lateral plane of a model for in-vitro studies on pineal gland. Material 1: Air. Material 2: Glass. Material 3:Rubber. Material 4: Pineal gland. Material 5: Attached skull. Material 6: Krebs–Ringer buffer was pumped through the glasscylinder receptacle.085222-4 Cen et al. AIP Advances 7, 085222 (2017)TABLE I. Thermal Properties Assumed for the Various Materials.Material ρ[kg/m3] Cp[J/kg·◦C] K[W /m ·◦C]1 1.3 1017 0.02342 2700.0 670 0.69803 36.9 3140 0.04204 1040.0 3700 0.57005 1810.0 1300 0.30006 1000.0 4180 0.5500FIG. 2. E-field (magnitude) distribution on the XY observation plane cutting the centre of the pineal gland in-vitro model(frequency = 1800MHz).FIG. 3. E-field (magnitude) distribution on the XZ observation plane cutting the centre of the pineal gland in-vitro model(frequency = 1800MHz).085222-5 Cen et al. AIP Advances 7, 085222 (2017)III. NUMERICAL EXAMPLEEquations (6) and (7) can be easily implemented on a computer. To illustrate effectiveness ofthe proposed method, the in-vitro study on pineal gland shown in Figure 1 in a sector of the radialwaveguide exposure system7 was conducted.It is calculated for 6 different materials, including the air surrounding the model, glass, rubber,pineal gland, attached skull, and Krebs–Ringer buffer. Table I lists the thermal properties of allmaterials.Figure 2–4 show the electric field distributions plotted across the centre of the model due toexcitation of 1800MHz. Determination of the electromagnetic heating source8 will not be discussedin this paper.FIG. 4. E-field (magnitude) distribution on the YZ observation plane cutting the centre of the pineal gland in-vitro model(frequency = 1800MHz).FIG. 5. Specific absorption rate (SAR) distribution inside the pineal gland in-vitro model. The XY observation plane is at thecentre of the model. The isolated pineal gland is exposed to a 1800 MHz TEM wave at 0.8 W/kg average SAR.085222-6 Cen et al. AIP Advances 7, 085222 (2017)The specific absorption rate distribution is evaluated as:SAR(i, j, k)=σ(i, j, k)[ˆEx2(i, j, k) + ˆEy2(i, j, k) + ˆEz2(i, j, k)]2ρ(i, j, k) (8)where σ(i, j, k) and ρ(i, j, k) are the conductivity and density of the tissue filling the (i, j, k) cell.Figure 5–7 show the SAR distributions inside this pineal gland in-vitro model.The temperature rise of the target model after 5 min exposure was calculated at 800 mW/kgaverage SAR in the small pineal organ. The initial temperature began from 37◦C. Figure 8–10 showFIG. 6. Specific absorption rate (SAR) distribution inside the pineal gland in-vitro model. The XZ observation plane is at thecentre of the model. The isolated pineal gland is exposed to a 1800 MHz TEM wave at 0.8 W/kg average SAR.FIG. 7. Specific absorption rate (SAR) distribution inside the pineal gland in-vitro model. The YZ observation plane is at thecentre of the model. The isolated pineal gland is exposed to a 1800 MHz TEM wave at 0.8 W/kg average SAR.085222-7 Cen et al. AIP Advances 7, 085222 (2017)FIG. 8. Temperature distribution on the XY observation plane cutting the centre of the pineal gland in-vitro model(frequency=1800MHz).FIG. 9. Temperature distribution on the XZ observation plane cutting the centre of the pineal gland in-vitro model(frequency=1800MHz).the computed temperature distributions on the XY, XZ, YZ observation planes, respectively. Theobservation planes are at the centre of the in-vitro model.From Figure 8–10, we can find the maximum temperature rise in the biological sample is verysmall, these results exclude the possibility of thermally induced health hazards from cell phoneradiofrequency radiation for a healthy person. The results agree with those of many other researchers.R Cooke et al show that use of mobile phones does not increase leukaemia risk;9 T Takebayashiet al. observed no increase in overall risk of glioma or meningioma in relation to regular mobile085222-8 Cen et al. AIP Advances 7, 085222 (2017)FIG. 10. Temperature distribution on the YZ observation plane cutting the centre of the pineal gland in-vitro model(frequency=1800MHz).phone use;10 The research by MJ Schoemaker suggests that there is no substantial risk of acous-tic neuroma in the first decade after starting mobile phone use;11 The result of F Malek et al.indicates that no negative health effect can be associated with electromagnetic field (EMF) expo-sure;12 The study by C Johansen provides no support for an association between mobile phones andocular.13Byeon and Back discovered that melatonin level increased as temperature increased whenrice seedlings were exposed to various temperatures for 1 hr.14 Melatonin which is secreted bythe pineal gland in the brain is a major regulator of core body temperature. Hence, tempera-ture rise due to EM exposure may cause body’s melatonin level to increase. Many experimentsdo show increased melatonin levels after exposure to magnetic or electromagnetic fields.15–17So hypothetically, the results of temperature rise in the pineal gland might indicate that mela-tonin could be a good mechanistic candidate to explain potentially deleterious or salubriouseffects of cell phone RF radiation. Melatonin is used to treat insomnia. Cohen et al proposedthe hypothesis that a decrease in melatonin levels might promote the development of breastcancer in humans.18 Melatonin has also been reported to exert additional functions in otherorgans.19–23IV. CONCLUSIONSimulation of temperature and electromagnetic field inside pineal gland cell was for the firsttime performed to illustrate effectiveness of the FVM method. The results exclude the possibility ofthermally induced health hazards from cell phone radiofrequency exposure. In future study, we willapply the method implicitly24 to 3D multi-material model with non-uniform grids.ACKNOWLEDGMENTSThe paper was supported by the National Natural Science Foundation of China (61370185).1 International Agency for Research on Cancer (IARC), Non-Ionizing Radiation, Part 2: Radiofrequency ElectromagneticFields, IARC Monogr Eval Carcinog Risk Hum (2013), 102.2 Report of Partial Findings from the National Toxicology Program Carcinogenesis Studies of Cell Phone RadiofrequencyRadiation in Hsd: Sprague Dawley SD rats (Whole Body Exposures), bioRxiv preprint first posted online May. 26, 2016.3 P. J. Roache, Computational Fluid Dynamics, Hermosa Publishers, 1976.085222-9 Cen et al. AIP Advances 7, 085222 (2017)4 H. H. Pennes, “Analysis of tissue and arterial blood temperatures in the resting human forearm,” J. Appl. Physiol. 1, 93–122(1948).5 W. Cen, R. Hoppe, Z. Q. Cai, Z. Yu, and N. Gu, “Accurate 3D multi-material EM-thermal modelling,” AIP Advances 7,025214 (2017).6 R. D. Richtmyer and K. W. Morton, Difference Methods for Initial Value Problems, New York: Wiley, 1967, [secondedition].7 N. Marcuvity, Waveguide Handbook, IEE ELECTROMAGNETIC WAVES SERIES 21.8 W. Cen and N. Gu, “Efficient solution on solving 3D Maxwell equations using stable semi-implicit splitting method,” AIPAdvances 6, 055005 (2016).9 R. Cooke, S. Laing, and A. J. Swerdlow, “A case-control study of risk of leukaemia in relation to mobile phone use,” BritishJournal of cancer 103, 1729–1735 (2010).10 T. Takebayashi et al, “Mobile phone use, exposure to radiofrequency electromagnetic field, and brain tumour: A case-controlstudy,” British Journal of Cancer 98, 652–659 (2008).11 M. J. Schoemaker et al., “Mobile phone use and risk of acoustic neuroma: Results of the Interphone case-control study infive north European countries,” British Journal of Cancer 93, 842–848 (2005).12 F. Malek, K. A. Rani, H. A. Rahim, and M. H. Omar, “Effect of short-term mobile phone base station exposure on cognitiveperformance, body temperature, heart rate and blood pressure of Malaysians,” Scientific Reports 5, 13206 (2015).13 C. Johansen, J. D. Boice, Jr., J. K. McLaughlin, H. C. Christensen, and J. H. Olsen, Mobile phones and malignant menomaof the eye, British Journal of Cancer 86, 348–349 (2002).14 Y. Byeon and K. Back, “Melatonin synthesis in rice seedlings in vivo is enhanced at high temperatures and under darkconditions due to increased serotonin N-acetyltransferase and N-acetylserotonin methyltransferase activities,” Journal ofPineal Research 56, 189–95 (2014).15 J. Bakos, N. Nagy, G. Thuroczy et al., “Urinary 6-sulphatoxymelatonin excretion is increased in rats after 24 hours ofexposure to vertical 50 Hz, 100 microT magnetic field,” Bioelectromagnetics 18, 190–192 (1997).16 A. Lerchl, A. Zachmann, M. A. Ali et al., “The effects of pulsing magnetic fields on pineal melatonin synthesis in a teleostfish (brook trout, Salvelinus fontinalis),” Neurosci Lett 256, 171–173 (1998).17 H. Lewy, O. Massot, and Y. Touitou, “Magnetic field (50 Hz) increases N-acetyltransferase, hydroxy-indole-O-methyltransferase activity and melatonin release through an indirect pathway,” Int J Radiat Biol 79, 431–435 (2003).18 M. Cohen, M. Lippman, and B. Chabner, “Role of pineal gland in aetiology and treatment of breast cancer,” Lancet 2,814–816 (1978).19 Y. L. Tain et al, “Melatonin prevents increased asymmetric dimethylarginine in young rats with bile duct ligation,” Journalof Pineal Research 48, 212–221 (2010).20 M. Pan, Y. L. Song, J. M. Xu, and H. Z. Gan, “Melatonin ameliorates nonalcoholic fatty liver induced by high-fat diet inrats,” Journal of Pineal Research 41, 79–84 (2006).21 P. Subramanian, S. Mirunalini, S. R. Pandi-Perumal, I. Trakht, and D. P. Cardinali, “Melatonin treatment improves theantioxidant status and decreases lipid content in brain and liver of rats,” Eur J Pharmacol 571, 116–119 (2007).22 Y.-L. Tain et al, “Melatonin regulates L-arginine transport and NADPH oxidase in young rats with bile duct ligation: Roleof protein kinase C,” Pediatr Res 73, 395–401 (2013).23 D. Thong-Ngam, S. Samuhasaneeto, O. Kulaputana, and N. Klaikeaw, “N-acetylcysteine attenuates oxidative stress andliver pathology in rats with non-alcoholic steatohepatitis,” World J Gastroenterol 13, 5127–5132 (2007).24 W. Cen, R. Hoppe, and N. Gu, “Fast and accurate determination of 3D temperature distribution using fraction-step semi-implicit method,” AIP Advances 6, 095305 (2016).

3D highly heterogeneous thermal model of pineal gland in-vitro study for electromagnetic exposure using finite volume method

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