Estimation of the optimum number and location of nanoparticle injections and the specific loss power for ideal hyperthermia

Hyperthermia is one of the most appealing methods of cancer treatment in which the temperature of tumor is elevated to reach a desired temperature. One of the methods of increasing tissue temperature is injection of nanoparticle fluids to tumor and applying alternative magnetic field, which is called magnetic nanoparticle hyperthermia method. The total number of injection points, as well as the their location within a tissue play a significant role in this method. Furthermore, the power of heating of a magnetic material per gram or specific loss power (SLP) is another important factor which needs to be investigated. As the uniform temperature of 43 °C is effective enough for a tumor regression in certain specific tissues, the inverse method is applied to find out both the number of injection points and their location. Furthermore, the effective amount of heat generated by nanoparticles is investigated by this technique. Two-dimensional cancerous brain tissue was considered, zero gradients on boundary conditions were assumed, and diffusion equation and Pennes equation, which is regarded as energy equation, were solved, respectively. Conjugate gradient technique as a one way of inverse methods is applied, and unknowns are investigated. The results illustrate that three-point injection with the best injection sites cannot induce a uniform temperate distribution of 43 °C, and although four-point injection can create a uniform temperature elevation, the amount of it cannot reach the 43 °C. Finally, the optimum locations of five-point injection which are ((0.80,3.24), (0.80,0.84), (2.00,2.00), (3.20,3.24), (3.32,0.84)) (all dimensions are in mm) in the studied domain with special loss power of 420 W/g, all of which are obtained after 36 iterations, demonstrate that these conditions can meet the requirements of the magnetic fluid hyperthermia and can be considered for the future usage of researchers and investigators.