The Lumped-Parameter Calorimetric Model of an AC Magnetometer Designed to Measure the Heating of Magnetic Nanoparticles

The assessment of superparamagnetic nanoparticle heating is crucial for effective hyperthermia. AC magnetometry can be used to determine the specific absorption rate (SAR) of nanoparticles, assuming proper calorimetric calibration. We show that an AC magnetometer developed in our laboratory can be used simultaneously as a calorimeter for calibrating measurements. An electrical circuit with lumped parameters that are equivalent to the non-adiabatic calorimeter and that incorporates the effects of heat flow from the excitation coil, the surrounding environment, and the sample is presented. Quantitative thermal system identification was performed using global optimization, which fitted the temperature measured by the three fiber-optic probes to the simulated temperature transient curves. The identified model was used to estimate the thermal power generated in the measurement sample using a resistor with a controlled current value. The results demonstrate significant error reduction, particularly at lower heating powers, where external heat transfer becomes more influential. At low heating power values (around 25 mW), the error was reduced from 16.09% to 2.36%, with less pronounced improvements at higher power levels. The model achieved an overall accuracy of less than 2.5% across the 20–200 mW calibration range, a substantial improvement over the corrected-slope method. The value of the true thermal power of nanoparticles can be obtained using the calibrated calorimeter.