Interpreting the magnetorelaxometry signal of suspended magnetic nanoparticles with Kaczmarz' algorithm

Magnetic nanoparticles in colloidal dispersions are important for biomedical applications like magnetic drug targeting, magnetic particle hyperthermia, and several imaging applications. For a physical understanding of these applications, the particles' hydrodynamic size distribution should be well characterized. Magnetorelaxometry is a fast method to determine this property, but until now had the drawback that a priori information, like a functional form of the expected size distribution, was necessary. Following recent advances, where Kaczmarz' algorithm was used to determine the core size distribution from static magnetization curves without any such assumptions, we present a similar study for the determination of the hydrodynamic size distribution. Here, the performance of several implementations of Kaczmarz' algorithm are investigated for both simulated and measured magnetorelaxometry data. Our results show that this method is able to determine the hydrodynamic size distribution in agreement with either the known input distribution, in the case of simulated data, or other size estimates determined with different methods such as thermal magnetic noise spectroscopy and dynamic light scattering in the case of measured data.