  Our purpose in this study was to present an integral-transform approach to
the analytical solutions of the Pennes's bioheat transfer equation and to apply
it to the calculation of temperature distribution in tissues in hyperthermia
with magnetic nanoparticles (magnetic hyperthermia). The validity of our method
was investigated by comparison with the analytical solutions obtained by the
Green's function method for point and shell heat sources and the numerical
solutions obtained by the finite-difference method for Gaussin-distributed and
step-function sources. There was good agreement between the radial profiles of
temperature calculated by our method and those obtained by the Green's function
method. There was also good agreement between our method and the
finite-difference method except for the central temperature for a step-function
source that had approximately a 0.3% difference. We also found that the
equations describing the steady-state solutions for point and shell sources
obtained by our method agreed with those obtained by the Green's function
method. These results appear to indicate the validity of our method. In
conclusion, we presented an integral-transform approach to the bioheat transfer
problems in magnetic hyperthermia, and this study demonstrated the validity of
our method. The analytical solutions presented in this study will be useful for
gaining some insight into the heat diffusion process during magnetic
hyperthermia, for testing numerical codes and/or more complcated approaches,
and for performing sensitivity analysis and optimization of the parameters that
affect the thermal diffusion process in magnetic hyperthermia.
