Heating Power of Millimeter-Sized Implanted Coils for Tumor Ablation: Numerical-Analytic Analysis and Optimization

Minimally invasive thermal ablation procedures of tumors with implanted devices are very promising, especially for the repetitive treatment of deep-seated tumors. The implanted devices are heated without contact by an alternating magnetic field from outside the patient’s body. In this paper, the heating power of millimeter-sized implanted coils is analyzed and optimized with a numerical-analytic analysis and the dependencies on spatial, electrical, and magnetic parameters are evaluated and presented for being able to choose the optimum implanted coil for a specific set of parameters. The analysis is done with focus on the implanted coils based on a homogeneous alternating magnetic field. A heating power of 1.5 W required for achieving an adequate rise of tissue temperature is determined in a thermal analysis and the corresponding specific absorption rate (SAR) is evaluated along with the power transfer efficiency (PTE) and the coupling coefficient for different types of implanted coils. For uncompensated implanted coils, a SAR of 306 mW/kg, a PTE of
$\mathrm {4.62\cdot 10^{-3}}$
and a coupling coefficient of
$\mathrm {2.49\cdot 10^{-3}}$
is achieved by a magnetic field strength of 1727 A/m, whereas a SAR of 1.84 mW/kg, a PTE of
$\mathrm {436\cdot 10^{-3}}$
and a coupling coefficient of
$\mathrm {2.3\cdot 10^{-3}}$
is achieved by a magnetic field strength of 134 A/m for serial compensated implanted coils. With this, the ratio of heating power to required magnetic field strength is maximized, which reduces the risk of unwanted heating of healthy tissue and other implanted devices and therefore enhances the safety as well as the well-being of the patients.