Research on Optimization Method of Magnetic Hyperthermia Based on Helmholtz Coil Device
Tang Yundong1, Ding Yubin1, Jin Tao2
1. College of Physics and Information Engineering Fuzhou University Fuzhou 350108 China; 2. College of Electrical Engineering and Automation Fuzhou University Fuzhou 350108 China
Abstract The treatment magnetic field usually presents an inhomogeneous distribution inside a real therapeutic equipment during magnetic hyperthermia, which will ultimately affect the treatment effects due to its unsatisfactory distribution of treatment temperature inside tumor region. However, previous literature has paid less attention to optimize the uniformity for magnetic field device and also to investigate its influences on the treatment effect during magnetic hyperthermia. Furthermore, the magnetic nanoparticles (MNPs) concentration under the same magnetic fluid dose is expected to have a value as small as possible in order to reduce the effect of the MNPs residual inside bio-tissue, which however was also rarely reported by the existing researches. This article investigates the therapeutic magnetic field for circular and square Helmholtz coil devices, analyzes the influence of magnetic field uniformity on the therapeutic effect by evaluating the temperature distribution of biological tissue due to the applied magnetic field, and also discusses the influence of different magnetic fields on the cumulative equivalent heating minutes at 43℃ under two different blood perfusion rates. In addition, this study proposes an improved particle swarm optimization algorithm considering several constraints in order to obtain the minimum volume fraction of MNPs at the injection point and the corresponding optimized properties for MNPs radius and magnetic field at this time. The proposed constraints involved in this study consist of the maximum safe temperature for treatment, the safe upper limit of treatment magnetic field, the size range of MNPs, and the effective conditions for MNPs heat generation. The partial differential equations involved magnetic field and temperature field are solved using finite element method for the proposed Helmholtz coil devices and a three-dimensional mouse model, respectively. The MNPs inside the proposed tumor region are assumed to have a Gaussian distribution centered on the injection point. Simulation results demonstrate that the final optimization results considering the proposed method meet the requirements of proposed constraints, which are 0.009 96 for the volume fraction of MNPs at the injection point, 50kA/m for the magnetic field intensity, 100kHz for the magnetic field frequency, and 7.005nm for the radius of MNPs during therapy. Both circular and square Helmholtz coils can generate a uniform magnetic field near the coil center while tend to have an inhomogeneous distribution away from the coil center. In comparison, the square Helmholtz coil presents a better uniformity in magnetic field distribution away from the coil center with respect to the circular one. This characteristic is also mirrored in the treatment temperature distribution and ultimately the treatment effect. In addition, the case considering the temperature-dependent blood perfusion rate presents a higher cumulative equivalent heating minutes at 43℃ than the case considering a constant one under the three different magnetic fields. The following conclusions can be drawn from the simulation analysis: (1) The circular Helmholtz coils can have a better performance in the magnetic field uniformity with respect to the square Helmholtz coil, and this characteristic is also true for the treatment temperature distribution and the treatment effect during magnetic hyperthermia. (2) The proposed method based on the improved particle swarm optimization algorithm can not only meet the safe criterions of maximum treatment temperature and the magnetic field but also obtain a far less volume fraction of MNPs than the classical value. (3) Temperature-dependent blood perfusion rate can result in an overall higher treatment temperature distribution and thermal damage for malignant tissue with respect to a constant one in the same therapeutic condition.
Tang Yundong,Ding Yubin,Jin Tao. Research on Optimization Method of Magnetic Hyperthermia Based on Helmholtz Coil Device[J]. Transactions of China Electrotechnical Society, 2023, 38(5): 1248-1260.
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2023, Vol. 38 
