Hyperthermia is a type of cancer treatment in which cancer cells are exposed to high temperatures (in the range 42--45°C). Research has shown that high temperatures can damage and kill cells by maintaining them in that range of temperatures for approximately thirty minutes. By killing cancer cells and damaging proteins and structures within them, hyperthermia may shrink tumors with minimal injury to normal tissues. In this research, the viability of the treatment is investigated by means of Pennes' bio-heat equation to model the heat diffusion in tissues for domains containing magnetic nanoparticles, which are the heat sources. The heating mechanism is the result of the magnetic relaxation of the particles (Brownian and/or Neel relaxation) by the application of alternating magnetic fields. The bioheat equation is solved for different shapes of the domain and heating conditions by numerical and analytical methods. A method for solving analytically bio-heat problems by means of free-space Green's functions is developed and applied to some particular problems. A parametric analysis was carried out to develop the relative influence of the parameters involved in the process on the temperature profile, like the generation rate, perfusion rate and distribution of the sources. This study shows that with heating rates already achievable, it is possible to reach the therapeutic temperature profile. Then, the limitations in the treatment would rely in questions of toxicity, targeting, among others.
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