Algorithm Analysis Of Harmonics Measurement Using Magnetic Nanoparticles’ Magnetization In AC Applied Field

This thesis researchs the Langevin function describing paramagnetic properties ofmagnetic nanoparticles(MNPs) by the technology of digital signal processing. This studyanalyses frequency spectrum of MNPs’ magnetization in AC applied field by discretizingand transforming the Langevin function in way of Fourier series. Each harmonic isproportional to the concentration of nanoparticles in the volume sampled. The ratio of apair of the harmonics is independent of concentration and have a relationship withtemperature. Thus it can be used to estimate the temperature for unknown or evenchanging concentrations. This paper uses algorithm of digital phase-sensitive detection(DPSD) and system identification based on least squares to detect the odd harmonicamplitude in magnetization of Magnetic Nanoparticles excited by AC applied fieldrespectively. In the view of the measurement precision and real-time, this paper analysesthe temperature is sensitive to every harmonic amplitude. It is expected to provide atechnology for precise tissue temperature measurement and have great significance in thefield of localized tumor heating and mediation of intracellular hyperthermia.Firstly, this paper discretizes the model of the magnetization of MNPs and establishsthe polynomial model of MNPs’ magnetization in AC applied field. In the weak staticapplied field，the susceptibility of magnetic nanoparticles obey the Curie paramagneticlaw. In the weak alternating applied field, every odd harmonic amplitude in themagnetization of MNPs has temperature sensitivity. Through the simulation, this studyhas determined quadrinomial theory model of the odd harmonic amplitude measurement.Secondly, in consideration of each harmonic relating with concentration andtemperature of MNP, this paper presents the method of picking up the harmonics of theMNP’s magnetization in the AC applied field by digital phase-sensitive detection(DPSD) algorithm. Through the DPSD parallel measurement and DPSD serial measurementmethods, this paper evaluates the result of every harmonic amplitude data under randomwhite noise environment. DPSD algorithm has remarkable character in sampling time forcalculation accuracy. Owing to using the sampling points to cross-correlation calculationrepeatedly, real-time performance of harmonic measurement is not satisfied.In consideration of the above questions, this paper presents the method of picking upthe harmonics of the MNP’s magnetization in the AC applied field by systemidentification algorithm based on the least squares and analyses the results of simulation.Although the real-time detection performance based on this method can track theharmonic change in different temperature, it’s very important that the correct selection ofthe sampling frequency is beneficial to the high order harmonic weak amplitude detectionunder the random white noise environment. It’s because undersampling will causeidentification precision is low, the oversampling cause computer truncation error whichgives rise to that the sufficient condition of algorithm is not met.Finally, this paper compares different characteristics and effect of two methods inpicking up the harmonics of the MNP’s magnetization in the AC applied field and putforward the use of the function relation between the harmonics can achieve thetemperature detection and imaging.