XIX Sympozjum Srodowiskowe PTZE - materialy.pdf

XIX Sympozjum PTZE, Worliny 2009
( ) ρ ω ( )
∇ −k∇ T = C T − T + Q + Q
(3)
b b b b ext met
where T is body temperature [K], k − the tissue thermal conductivity [W/(m·K)], ωb − the
blood perfusion rate [1/s], Cb − the blood specific heat, Tb − the blood vessel temperature,
Qmet − the metabolic heat generation rate [W/m 3 ], and Qext − the external heat sources [W/m 3 ].
The usual boundary condition associated with the heat transfer process in the context of
hyperthermia can be given by
n ⋅( −k∇ T) = h( T −T)
(4)
air
on boundary Γ, where h is the heat transfer coefficient [W/(m 2 ·K)], Tair is the temperature of
the surrounding air [K].
Computational results
The hyperthermia arrangement in two dimensions as given in Fig. 1 is considered. The
dimensions and physical parameters of the model are given in following tables (Tables 1 − 2)
[4, 5, 6]:
Table 1. Physical parameters of tissues taken into numerical model
Tissue εr
σ
[S/m]
k
[W/(m·K)]
Qmet
[W/m 3 ]
Human body 29.6 0.053 0.22 300
Table 2. Physical parameters of blood taken into bioheat equation
ρb
Cb
Tissue
[kg/m 3 ] [J/(kg·K)] [K]
ωb
[1/s]
Blood 1060 3639 310.15 in body 0.005
The whole computational domain was divided into triangular finite elements and appropriate
boundary conditions were introduced. The exciting current in the coil is Imax = 4.5 [A], and
frequency is f = 100 [MHz]. Moreover, the heat transfer coefficient is h = 10 [W/(m 2 ·K)] [25],
and the air temperature surrounding the body is Tair = 293.15 [K]. Radius of the exciting coil
with current Imax has value r = 0.6 [m].
93
Tb