A Computational Investigation of Magnetic Nanoparticle induced Hyperthermia using the Finite Volume Method

Abstract

In this work magnetic nanoparticle induced hyperthermia has been computationally analyzed using the finite volume method. This work is focused on analysis of variation in treatment parameters (frequency and amplitude of alternating magnetic field, and dose of magnetic nanoparticles injected). The frequency and amplitude values considered for analysis are in accordance with the safe range mentioned in literature. The analysis has been carried out for uniform as well as nonuniform spatial distribution of intratumorally injected magnetic nanoparticles. Gaussian distribution has been used to model nonuniform distribution of magnetic nanoparticles. Nonuniform distribution of magnetic nanoparticles has been used for cases of single-point as well as multi-point injection. Magnetite nanoparticles have been considered for analysis. Computation has been carried out for one-dimensional, two-dimensional, and three-dimensional geometric models. For the one-dimensional model that consists of only healthy tissues, numerical solutions have been obtained for time dependent as well as steady state cases. Results for both cases have been validated with the analytical solutions. The two-dimensional model, consisting of a tumor surrounded by healthy tissues, has also been analyzed for steady as well as time dependent cases. The results obtained using finite volume method agree well with those reported in literature, using lattice Boltzmann method, and finite element method. Variation in amplitude of the alternating magnetic field is initially analyzed on the three-dimensional model, which also consists of a tumor surrounded by healthy tissues. 5 kA.m-1, 7.5 kA.m-1, and 10 kA.m-1, are the values of amplitude that were considered in analysis. Results revealed that with increment in magnetic field amplitude, temperature within the tumor also increases. Similar results were obtained when frequency values of, 50 kHz, 75 kHz, and 100 kHz, were used. Highest increments in temperature were observed for single point injection, and lowest with uniform distribution, with increase in both amplitude and frequency of the magnetic field. It was also observed that with multi-point injection a more uniform temperature distribution is obtained, in contrast to single-point injection and uniform distribution of nanoparticles. Variation in nanoparticle dose is analyzed using the values, 4 mg of magnetite / cm3 of tumor, 5 mg of magnetite / cm3 of tumor, and 6 mg of magnetite /cm3 of tumor. Results reveal that increments in nanoparticle dose also result in increase in temperature. Greater variation in temperature is observed with variation in treatment parameters if the injected nanoparticle mass at a specific location is also high. Temperature variation is more pronounced with variation in amplitude and frequency, than it is with nanoparticle dose.