Image quality in the new imaging modality magnetic particle imaging (MPI) heavily relies on the quality of the magnetic nanoparticles in use. Therefore, it is crucial to understand the behaviour of such particles. A common technique to analyze the behaviour of the particles is magnetic particle spectrometry (MPS). However, most spectrometers are limited to measurements at a single or multiple discrete excitation frequencies. This paper introduces a frequency-tunable spectrometer, able to perform measurements in the range of 100 Hz - 24kHz.
In 2005 the upcoming imaging modality magnetic particle imaging (MPI) was presented by Weizenecker and Gleich . Until now, a lot of effort has been made to improve the imaging systems. Sensitivity enhanced systems like field-free line imaging, as well as better signal processing techniques are just two of the many aspects that have been adressed. Nevertheless image quality in MPI not only depends on the quality of the imaging system, but likewise on the quality of the magnetic nanoparticles. The influence of magnetic nanoparticle properties on imaging quality has been discussed for example by Ferguson et al. . A common method to determine the properties of magnetic nanoparticles is magnetic particle spectroscopy (MPS) as presented by Biederer . However, modern MPS systems are only capable of measuring at discrete frequency steps. Most systems are limited to one excitation frequency, others to multiple discrete frequencies . The following sections describe a measurement setup which is capable of carrying out MPS measurements with a freely tunable excitation frequency in the range of 100 Hz - 24 kHz. This reveals the possibility to determine different properties of the nanoparticles, such as: the influence of Brownian and Néel rotation on signal quality, the frequency-dependent hysteresis and its related dissipation losses, the hydrodynamic volume of the particles, the temperature of the sample or the viscosity of the medium surrounding the nanoparticles .
The most published signal chain of an MPS system is shown in Figure 1. It consists of a personal computer (PC) which generates the excitation signal. This signal is amplified by a power amplifier to supply the necessary current to produce a specific field strength. The excitation signal has to be filtered by a bandpass-filter to eliminate unwanted signal frequencies, which may couple into the system by induction. Those frequencies can be hard to distinguish from the harmonics produced by the particles. The send coil’s impedance is matched by a set of capacitors to compensate the reactance of the coil and match the resulting load to the power amplifier’s optimal load. This ensures a high efficiency of the power amplifier. Due to the fact that the excitation field induces a signal orders of magnitude higher than the particle signal, a bandstop-filter has to be used to reduce the excitation signal. The filtered signal is amplified by a low-noise amplifier and finally fed back to the PC for further analysis. This setup is limited to a single excitation frequency due to the bandpass and lowpass filtering stages, which have to be made of passive electrical components to avoid nonlinear effects and prevent the distortion of the particle signal. To overcome this limitation the send and receive chain have to be modified. These modifications are presented in the upcoming section.
To allow a free choice of the excitation frequency in a given frequency range, it is required to get rid of frequency limiting structures like lumped filters and the concept of an ideal impedance matching. The two major issues which have to be adressed are: distribution of the required current in the send coil, which is equal to restraining the power amplifiers load to a specific range and elimination of the excitation signal in the receive chain, allowing the measurement of the particle signal.
For a frequency-independent elimination of the excitation signal a cancellation technique described by Graeser et al.  has been implemented. The idea is to build two identical measurement chambers. During the measurement process, in one of the chambers the particles are inserted and the other one is left empty. The send coils of the chambers are connected in series, providing the same current in the coils and accordingly the same excitation field. The receive coils are connected in series as well, but with subtractive polarity, thus the excitation signal cancels out. As the particle signal is only induced in one receive coil it is unaffected by the cancellation and is the only signal left. The setup is shown in Figure 2. The dots next to the coils denote the same instantaneous polarity of the coils. In a real setup the cancellation is not ideal as the chambers will differ slightly due to manufacturing inequalities. Additionally, environmental influences might vary in the chambers. The cancellation is best when the magnetic flux of the excitation signal is equal in both receive coils. Maximal attenuation can be achieved by adjusting the coupling factors of send and receive coil in one chamber to match the coupling factors of the second.
The limiting factor of an amplifier is its output power. To produce a sufficient current and a desired field strength, an apparent power given by
is required. Here I is the root mean square value of the current, Z is the complex load impedance and î is the current amplitude. The load of two coils in series is given by the absolute value of the sum of their complex impedances
where RL1 and RL2 are the equivalent series resistances L1 and L2 are the inductivities of the two send coils respectively. The frequency f of the signal is related to the angular frequency ω by ω = 2πf. The electrical parameters of the send coils are measured and the required current to produce a magnetic field amplitude of 10 mT is determined by simulation. The values are shown in Table 1. The frequency range is split into four measurement ranges. For one frequency in each of the measurement range the system’s apparent power is minimized by a capacitor in series connection to the coils. The measurement ranges, the frequencies for which the apparent power minimization is done and the corresponding capacitor values are shown
|Parameter||Coil 1||Coil 2|
|Equivalent series resistance||34.5mΩ||28.7 mΩ|
|Required current amplitude||13 A|
in Table 2. In Figure 3 the logarithmic apparent power of the different setups over the full frequency range is shown and the related measurement ranges are highlighted. As it can be seen the apparent power stays below 500 V A for every measurement range. The minimization frequencies are chosen to low. This is done to ensure the resulting load is inductive for most measured frequencies, because capacitive loads may lead to instabilites in the amplifier’s operation . The power amplifier used to drive the coils is an AE Techron 7224 amplifier with a maximum power output of 1000 W into an optimal load of8 . It is necessary to oversize the amplifier concerning the power, as the stated load impedance is almost never the optimal load to achieve the maximum output. In addition, the load is reactive for most frequencies, which means the signal from the amplifier is partially reflected back to the amplifier, leading to increased heating of the amplifier and limiting the maximum applicable power to the load.
|1||100 Hz – 8.5 kHz||-||-|
|2||8.5 kHz – 14 kHz||9160 Hz||4µF|
|3||14 kHz – 19 kHz||14 700 Hz||1.5µF|
|4||19 kHz – 24 kHz||19875 Hz||0.83 µF|
The resulting setup of the spectrometer is presented in Figure 4. The capacitors are connected in series right after the power amplifier, each with the possibility to be bypassed with a short connection. The send coils are connected in series as well, whereas the voltage over one coil is measured using a voltage divider. If the voltage differs from the expected value, the excitation voltage is adapted accordingly. The receive coils are connected in a subtractive polarity manner such that the excitation signal cancels out. Then the particle signal is amplified by the SR560 low-noise amplifier and measured by the PC.
The spectrums of two exemplary particle measurements are shown in Figure 5. The amplitudes have been normalized and plotted against the k-th harmonic of the excitation frequency. Measurements have been carried out for 49 frequencies starting at 100 Hz, 500 Hz and continuing in steps of 500 Hz to 24kHz. The particle signals have been measured succesfully for every frequency and every particle measurement has been corrected by a preceding empty measurement.
In conclusion a setup for a frequency-tunable spectrometer in the range of 100 Hz - 24kHz has been introduced. Based on particle measurements it could be shown that the spectrometer is working as intended and is able to determine the particle spectrums accurately. This allows for further investigations such as: particle performance, relaxation effects or dissipation losses.
We acknowledge the support of the Federal Ministry of Education and Research, Germany (BMBF) under the grant numbers 13GW0069A and 13N11090.
Conflict of interest: Authors state no conflict of interest. Material and Methods: Informed consent: Informed consent has been obtained from all individuals included in this study. Ethical approval: The research related to human use has been complied with all the relevant national regulations, institutional policies and in accordance the tenets of the Helsinki Declaration, and has been approved by the authors’ institutional review board or equivalent committee.
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