Thermodynamics of movable inductively heated seeds for the treatment of brain tumors

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Abstract
A thermodynamic study is presented of temperature distributions created by an inductively heated 6‐mm‐diam Ni sphere imbedded in vivo and in vitro into porcine brain tissue. This study was performed in support of the development of a system that creates localized heat‐induced lesions in deep‐seated brain tumors. In this system, a magnetic “seed” will be remotely repositioned within the brain by an externally produced magnetic field. Convective effects of a hot moving seed will produce a different thermodynamic situation than that arising from an array of static implants. In this work, a study is presented of part of the expected change, in which a static sphere is heated to high temperature. Measurements were made of the temporal and spatial dependence of the temperature rise in the vicinity of the heated sphere, in vivo in four animals and in one that was euthanized immediately prior to experimentation. These results are used for parameter estimation with a theoretical model based on a point source solution to a form of the thermal diffusion equation, i.e., the “bioheat transfer equation.” With this model thermal distributions from a power source of arbitrary geometry can be found using appropriate integration methods, and the method has widespread applicability. Estimates of blood flow rates, tissue thermal conductivity, and seed power absorption were found using the parameter estimation algorithm. The estimated blood perfusion exhibits a step increase following the first heating in multiple heating experiments. Thermal conductivity estimated using data from the nonperfused (in vitro) animal is 0.6 W/m °C. Seed power absorption is estimated correspondingly to be 0.9 W, a result confirmed independently with calorimetry. Statistical uncertainty is established for the radial decrease of the tissue temperature rise created by this method. This result allows estimation of a cell death boundary uncertainty of 0.6 mm, caused by fluctuations in power delivered to the seed, uncertainty in the temperature probe placements, and thermal properties such as blood perfusion and tissue thermal conductivity.

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