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FDTD HEAD MODEL OF THERMAL EFFECTS OF ELECTROMAGNETIC RADIATION
Stanislav Lovás and Elena Cocherová Department of Radioelectronics, FEI STU Ilkovičova 3, Bratislava, Slovak Republic E-mail: elena.cocherova@stuba.sk, st.lovas@centrum.sk Abstract: This paper deals with thermal electromagnetic radiation effects on human organism. Heat propagation for specific case for 1D model of human head iscalculated by use of the finite-difference time-domain (FDTD) method. I. Introduction

Human being meets electromagnetic (EM) radiation every day. Absorption of EM fields causes temperature rise in the human tissue. Heat load of human body in everyday life varies approximately from 1 W.kg-1 to 10 W.kg-1, depending on subject activity [1]. Exposure of healthy humans at the whole-body SAR of 4 W.kg-1for 20-30 minutes at normal conditions increases the body temperature in the range of 0.1-0.5 °C [1]. Measurement of the body SAR and the related temperature increase in living organisms is in general difficult, if not impossible, so appropriate methods for numerical evaluations must be used. II. Heat propagation equation

Heat propagation is described by equation [2] ∂T ∂T 2 =α 2 (1) ∂t ∂xwhere α is diffusivity of tissue: k α= (2) ρC and where T is temperature (K) ρ is mass density of tissue (kg.m-3) C is specific heat capacity (J.kg-1.K-1) k is thermal conductivity (W.m-1.K-1). The variable T denotes T(x,t), i.e. value of temperature in the space point x and in the time t. Heat equation for biological objects must also include additional terms [3]: ∂T (3) ρC = ∇(k∇T ) +WM − B(T − Tb)+WEM ∂t where WM is tissue metabolism (W.m-3) B is related to blood perfusion rate (W.m-3.K-1) Tb is blood temperature before entering the tissue (K) WEM is power of EM radiation absorbed by volume unit (W.m-3). Power of EM radiation absorbed by volume unit is: WEM = ρ ⋅ SAR (4) where SAR is specific absorption rate (W.kg-1).

III.

FDTD representation of heat equation

We use forward-timecentered-space (FTCS) scheme [4] for heat equation representation in discrete time and discrete space (Fig. 1).
t n n-1 known temperature node unknown temperature node

m-1 m m+1 0 Fig. 1 Forward-time centered-space scheme.

x

Second derivation in node m is approximated as ∂ 2T Tm+1 − 2Tm + Tm−1 ≈ h2 ∂x 2 The term for time derivation of temperature in time node n is approximated as n n −1∂T T − T ≈ ∂t τ
n Tm =

(5)

(6)

Substituting the terms (5) and (6) to heat equation (1), we get discrete FTCS representation

ατ
h
2

(T

n−1 m+1

n n−1 n − 2Tm −1 + Tm−1 )+ Tm −1

(7)

Similarly, bioheat equation (3) gets form kτ n (Tmn+−11 − 2Tmn−1 + Tmn−−11 )+ Tmn−1 + τ (WM − B(Tmn−1 −Tb )+WEM ) Tm = 2 ρCh ρC
where

(8)

τ
h n m

is time step (s) is space step (m)is discrete time variable ( x = m ⋅ h ) is discrete space variable ( t = n ⋅τ ).

Thermal exchange between blood and tissue relates to perfusion of blood through the tissue. The tissue-specific parameter B and blood temperature Tb have significant influence to tissue temperature.
IV. Model of the human head

We used a simple 1D model of human head (shown in Fig. 2). The spatial x-axis iscovered by uniformly arranged points, with distance h = 0.01 m, i.e. the length of spatial step is 1 cm. For computed region 90 cm long we used 90 space points. The time axis is divided with time step of length τ = 0.01 s, and total number of time points was 180 000, what represents time 1 800 s, i.e. 30 minutes. On the right side of head (x = 60 cm), we assume absorption of EM radiation of SAR 20W.kg-1. Initial temperature of the head tissues was 37 °C, surrounding air was of 20 °C. The blood temperature before entering the tissue was Tb = 37 °C. Heat propagation due to air convection was not assumed in the model.

0 bone skin air

30 31 32 brain

58 59 60 bone skin air

90 x (cm)

Fig. 2 Model of head in one dimension.

Material parameters used in the model are summarized in...