FPGA-based RF interference reduction techniques for simultaneous PET–MRI

The basic idea of the clock phase shift method is to modify the emitted RF fields by applying clock phase shifts between the clocked components of the PET detector. Since our PET detector consists of a plurality of clocked components emitting RF fields and thus contributing to the effective emitted field, the pattern of the field can be modified due to the superposition principle by applying the aforementioned phase shifts. This way, the emitted RF field pattern, which couples to the MRI RF coil, can be altered and the coupling of the externally applied RF fields can be reduced, thereby resulting in less interference between the PET system and the MRI RF receive chain. Here, the coupling is defined by the coefficients (determined by the overlap integral or coupling integral) of a mode expansion of the externally emitted fields in the mode basis function of the RF coil. A smaller coupling coefficient results in a decreased energy transmission efficiency due to the aggravated excitation of the RF coil's modes.

Figure 4 depicts the resonance spectrum of our bird cage RF coil, which was measured with a network analyser (Agilent E5071C ENA, USA). It visualises the different resonance modes of the coil. The energy of RF fields with frequencies corresponding to these modes is transmitted with a high efficiency into the coil. The mode which is highlighted with a grey-shaded area provides a homogeneous RF field distribution and is therefore used to generate the B₁ field required for spin excitation. The frequency of this mode is tuned to match the resonance condition (at 3 T:  ∼127.78 MHz). The other modes (visible at lower frequencies), not providing a homogeneous distribution, are not used for MRI acquisition purposes. Therefore, the MRI receive chain includes a band-pass filter around the 127.78 MHz mode to suppress the energy potentially transferred via the lower modes.

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The clock frequency shift approach aims at RF interference reduction by shifting the frequencies of PET-detector-related clock signals away from the homogeneous coil resonance mode to reduce EM field amplitudes at the resonance mode frequency and thus reduce the noise coupling into the coil to a minimum.

In a first step, we analysed this technique regarding its feasibility by implementing a model based on the sensor tile of an SDM: according to the arrangement of the sensor dies on a sensor tile (see figure 5(a)) and since all sensor dies are clocked via single-ended clock lines, we modelled a sensor tile as a system of 16 EM field emitters. As a simplification, each emitter is described as a magnetic dipole sender, resulting in a dipole emitter system with the same spatial arrangement as the sensor tile structure (see figure 5(b)). Based on this model, we calculated the emitted magnetic field distributions using MATLAB in planes parallel to the sensor tile surface to study the compensating superposition effect of the dipole system with clock phase relationships between dipoles that are out of phase (unequal to zero). Here, we focused on two example systems: an in-phase model, in which the phase relation between neighbouring dipoles (sensor dies) is set to ${{0}^{{}^\circ}}$, and a checkerboard model. In the latter, the phase relation between neighbouring dipoles is set to ${{180}^{{}^\circ}}$ (see figure 5(c)).

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In order to investigate the noise induction originating from external interferences to a birdcage resonator, the field coupling was simulated using a finite element method (FEM) toolkit (FEKO EM Software and Systems (www.feko.info)). Using this software toolkit, we implemented an FEM model of our PET-transparent mouse coil (see figure 6). Both phase pattern models were added via a modelled dipole arrangement in front of the RF screen in the simulation model, and the induced current distribution on the RF resonator was simulated for both phase patterns. To investigate the coupling at an operating point at which the resonator accepts external energy with most efficiency, we set the dipole frequency to the resonance frequency of the simulated RF coil.

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To investigate the impact of the sensor die clock frequency alternation with regard to resulting RF fields coupled into the MRI RF coil, an SDM was operated at different sensor die clock frequencies in addition to the typical sensor die clock frequency of 200 MHz. First, we chose a frequency equal to the Larmor frequency of the 3 T MRI because we expect the impact regarding RF field coupling into the MRI RF coil to be highest at this frequency, thereby demonstrating the influence of the sensor tile clock frequency related to the RF noise picked up by the MRI. Second, to study noise coupling for a clock frequency within the sensitive bandwidth of the MRI, but with less impact compared to a clock frequency at the Larmor frequency, 140 MHz was added for our measurements. Third, 100 MHz was chosen because its first harmonic is equal to the typical sensor die clock frequency of 200 MHz. Finally, we chose 160 MHz as a candidate located between clocking frequencies in the MRI-sensitive frequency bandwidth and the typical DPC sensor clock frequency.

The MATLAB-based calculation presented in section 3.2.1 was used to study EM field emission changes upon modifications of the sensor die clock phase at stack level. However, this does not take into account all other electronic components and connectors of the complete stacks as well as the SPU board, which contribute to the overall field emission in addition to single sensor tiles. Therefore, the scope of our measurements to study phase-pattern-related influences was extended by including a complete SDM equipped with six stacks rather than a single detector stack. For the measurements with an SDM, we applied sensor clock phase variations at SDM level, meaning that all sensor dies of a sensor tile are clocked in phase and that a fixed clock phase relation is kept between adjacent sensor tiles of an SDM. To remain consistent with the clock phase pattern chosen for the MATLAB calculation at stack level, measurements with an SDM were performed with a phase shift of ${{180}^{{}^\circ}}$ between adjacent stacks, resulting in a checkerboard pattern as shown in figure 7(b). The measurement results of emitted field amplitudes and field pattern obtained with firmware designs applying clock phase shifts were compared qualitatively to reference measurements where no phase shifts were present.

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As we used a single-SDM configuration for our investigations, the refCLK input signal of the SPU FPGA is not provided by the CSU. Instead, the refCLK signal for the SPU as well as the stack FPGAs is sourced by the 100 MHz oscillator residing on the SPU board. Clock signal frequencies and phases for clocking and data communication between the FPGAs within the SDM are kept identical between the single-SDM operation and the full-PET-ring operation. To obtain the desired clock and phase settings, the firmware design of the stack FPGAs is modified in such a way that the FPGA clock generator (a phase-locked loop) feeding the clock inputs of the sensor dies and clocking the FPGA-internal data processing chain is programmed to our frequency and phase shift needs. These clocking modifications thus only directly affect parts of the stack FPGA's digital logic and the single-ended signal traces between the interface board and the sensor tile.

The modified FPGA designs undergo synthesis, mapping and routing for the stack FPGA platform using Xilinx ISE tools (Xilinx Inc. (www.xilinx.com)). Afterwards, the resulting bit-file streams are converted into XSVF format. This allows for a stack FPGA configuration via the Hyperion software on the control PC, which communicates with an XSVF-JTAG programmer residing within the SPU FPGA firmware design. This avoids the need to access the SPU board of an SDM with an external JTAG programmer so that the SDM may remain entirely untouched during measurement series using different clock configurations.

To ensure that the PET data acquisition is correctly working with our modified firmware designs, we made singles measurements using one SDM with different firmware designs yielding sensor die clock frequencies and clock phase patterns as given in sections 3.3.1 and 3.3.2 and one ²²Na source with an activity of 3.95 MBq. The sensor die configuration parameters and operating conditions are set to values we typically use for PET measurements as described in Schug et al (2015), section III D. The 'center-of-gravity (CoG) with adaptive corner extrapolation' (COG-ACE) algorithm (Schug et al 2015) was used to perform off-line PET singles clustering on the acquired raw PET data sets. The firmware design clocking the sensor dies in phase at 200 MHz is the one typically used for the DPC sensors and serves as the reference design.

The SDM operation for all other measurements presented in this paper is as follows. A single SDM is directly connected to a control PC running Hyperion software and all FPGAs of the SDM are configured after SDM power-up. The sensor die configuration settings correspond to those as described above. Afterwards, the data acquisition is launched, during which RF-field-related measurements are made.

For a detailed RF field emission characterisation, we used a spectrum analyser (Agilent N9320B, USA) in combination with a magnetic-field probe (Langer EMV, RF-R 400-1, Bannewitz, Germany) which is round-shielded with a diameter of 25 mm. In contrast to measurements with the MRI system, these measurements allow the acquisition of broadband emission spectra to obtain a better overview on the distribution of amplitude magnitudes over the measured frequency range. The different frequency designs were tested by acquiring emission spectra in the range from 50 MHz to 250 MHz. For these measurements, the magnetic-field probe was positioned on the top centre of the SDM and as close as possible to the SDM housing (see figure 8).

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In addition to the amplitude measurement, the magnetic field component of the RF field pattern emitted by an SDM was measured and the result was visualised as a field map covering all magnetic-field probe measurement positions of one plane. We acquired field maps for the x and y components of the emitted $\vec{H}$ field on planes around the SDM (lateral surfaces of a cuboid) for a frequency range of  ±100 kHz around the sensor die clock frequencies (section 3.3.1). These maps were used to analyse changes in emitted RF field patterns depending on the chosen clock frequency and clock phase patterns and help to locate parts of the SDM which act as strong RF field emitters.

The magnetic-field probe was attached to an XYZ table (OWIS, Germany) enabling positioning in 3D space around the SDM under test and thus the acquisition of RF field patterns as shown in figure 8. All cuboid planes were covered by the probe by first measuring the top and left planes of the SDM (see figure 9) and then turning the SDM through ${{180}^{{}^\circ}}$ to repeat the measurement with the left plane becoming the right one and the top plane becoming the bottom one to complete the cuboid. The probe was moved 35 cm along the x, 10 cm along the y, and 9 cm along the z axis, thereby covering 2769 measurement points with a step of 5 mm. As the SDM was turned through ${{180}^{{}^\circ}}$ to measure the field pattern in the other two lateral planes of the SDM, the total number of measurement points is 5539, covering all four lateral planes of the SDM.

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We used a clinical MRI scanner (Achieva 3.0 T, Philips, The Netherlands) to evaluate the implemented frequency and phase pattern modifications with the full MRI acquisition chain (see figure 10). The carbon fibre shielding was removed to allow for larger differences in coupled RF noise for reasons of clarification between different measurement results. To evaluate the RF field emission of an SDM for different sensor die clock frequency and phase scenarios with regard to RF noise coupling into the MRI RF receive chain, dedicated spurious noise scans with the MRI and a PET-transparent Tx–Rx mouse coil (12-leg birdcage resonator, high pass) (Weissler et al 2015a) were performed. These MRI scans allow us to quantify the noise signal amplitudes as a function of frequency in the frequency region to which the MRI RF receive chain is sensitive. The measurement protocol is based on sequences provided by the MRI vendor and consists of five turbo-spin-echo (TSE) sequences (${{T}_{\text{R}}}$/${{T}_{\text{E}}}$ 1044/256 ms, turbo factor (echo train length) 32, acquisition matrix $1024\times 1024$, bandwidth per pixel 180 Hz) executed with shifted frequency ranges to cover a total continuous bandwidth of 1 MHz with the Larmor frequency as the centre frequency. As the vendor-provided MRI protocol includes RF pulse excitation (flip angle ${{1}^{{}^\circ}}$), the protocol was modified to exclude any MRI RF excitation so that noise measurement results are not affected by the presence of any subjects such as MRI phantoms in the MRI FoV, which provide RF signal due to MRI RF excitation (Wehner et al 2015). For these studies, the SDM was positioned on the most sensitive PET gantry SDM location regarding PET-related noise coupling into the RF coil. The location was determined by performing a noise scan using the SDM with the reference FPGA design (sensor die clock frequency 200 MHz) for all ten SDM positions of the gantry.

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The impact of the DPC sensor clock frequency variation on MRI was visualised by scanning a cylindrical phantom containing 20 ml of a CuSO₄ solution within the Tx–Rx mouse coil. We prepared a 2D TSE sequence (${{T}_{\text{R}}}/{{T}_{\text{E}}}=400/157.46$ ms, flip angle ${{90}^{{}^\circ}}$, turbo factor (echo train length) 12, voxel size  =  $0.07\times 0.07\times 0.5~\text{m}{{\text{m}}^{3}}$, number of slices 1, FoV size $80\times 80~\text{m}{{\text{m}}^{2}}$, acquisition matrix $1144\times 1144$, reconstruction matrix $1600\times 1600$) aiming at very high-resolution MR images with low SNR in order to visualise SNR differences. The SDM was again mounted without RF shielding on the gantry at the SDM position where the PET-related noise coupling to the RF coil was determined to be most sensitive and MRI scans were performed. Signal intensity values were determined along a horizontal line profile with a line width of 50 pixels, which crossed the phantom at its centre. Afterwards, the signal intensity values were normalised to the mean intensity at the phantom position and intensity values were averaged over ten histogram bins. With the plots normalised to the phantom signal intensity, the mean values of the noise level for each plot were calculated to determine changes in noise floor related to the SDM operation with different sensor die clock frequencies.

All stack firmware designs generating sensor die clock frequencies different from the typically used frequency of 200 MHz (with all dies clocked in phase) as described in section 3.3.1 were successfully tested with regard to expected clock frequency and phase relationships using an oscilloscope (Tektronix MSO4104, USA). In figure 13 are shown the mean singles rates for firmware designs yielding the sensor die clock frequencies described in section 3.3.1. They vary between 115.4 and 118.3 kcps. The mean singles rates for the cases of in-phase and checkerboard-phase patterns at the same clock frequency of 200 MHz are 119.7 kcps (standard deviation (STDd) 2.6 kcps) and 120.1 kcps (STDd 3.2 kcps), respectively.

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Figure 14(a) shows the results of the EM emission measurements made with the laboratory bench setup using the spectrum analyser for all tested sensor die clock frequencies. It is clearly visible that the modification of the die clock frequency enables an alternation of the emitted spectrum. With respect to the sensitive bandwidth of the MRI receive chain (depicted by the grey-shaded bar in figure 14), the die clock frequency resulting in lowest amplitudes around the Larmor frequency is the one at 160 MHz (red), followed by the one at 100 MHz (light blue). Aside from the intentioned worst-case scenario using a die clock frequency of 127.78 MHz (yellow), equal to the Larmor frequency, the worst performance in terms of highest amplitudes within the MRI-sensitive bandwidth is observed with the design clocking the dies at 140 MHz (green). The RF emission distribution is shown in more detail in figure 14(b) for the bandwidth of the 3 T MRI as covered by MRI noise scans for an bandwidth of 1 MHz around the Larmor frequency as described in section 3.4.3. The worst-case scenario was not included in figure 14(b) to better depict the spectrum amplitude differences between the sensor die frequencies different from the Larmor frequency of the 3 T MRI system.

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The measurement results of the RF-field-related magnetic field component obtained for an in-phase and a checkerboard-phase pattern at SDM level and a sensor die clock frequency of 127.78 MHz are shown in figure 15 (x component of the emitted H field) and figure 16 (y component of the emitted H field). In both figures, the four planes of a measured H-field component are the following from top to bottom: bottom, right, top and left sides of the SDM. The application of a checkerboard-phase pattern leads to changes in the emitted magnetic field pattern and amplitudes when comparing the H-field component H_x as well as H_y between the two clock phase patterns.

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The noise scan results obtained with the MRI using different sensor die clock frequencies are summarised in figure 17. Least noise was coupled into the MRI receive chain when the PET data acquisition chain of the SDM was operated with clock frequencies of 100 MHz and 160 MHz. A frequency of 140 MHz led to the worst case out of all chosen frequencies. In addition to the noise floor being raised to 350 floating point (FP) values, a distribution of distinct FP measurement points is spread between 350 and 460 FP values. In figure 17, the measurement results marked with black circles represent the MRI noise floor measured with a powered-off SDM.

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The noise measurement comparison between in-phase pattern and checkerboard-pattern clocking is depicted in figure 18(a). Both measurements resulted in Lorentzian line shapes due to the clock frequency being at the Larmor frequency at 3 T. The noise floor ratio (see figure 18(b)) for the frequency range shown in figure 18(a) is in the range of 0.5–0.6, meaning that the noise generated with the checkerboard pattern is reduced by almost a factor of two compared to the in-phase pattern.

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In figure 19 are shown three MR images which were acquired while the SDM was powered off (reference scan, image figure 19(a)), while the SDM was acquiring data with the DPC sensors clocked at 160 MHz (image figure 19(b)) and during SDM data acquisition with a sensor die clock frequency of 140 MHz (image figure 19(c)). The image quality is deteriorated in image (b) compared to (a) and is worst in image (c).

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The clock-frequency-dependent impact on the noise floor is distinguishable via the line profile determined for the three different MR images as shown in figure 20. The noise floor is lowest for the reference scan (noise mean value $0.722\pm 0.004$, SNR 1.385). When the SDM is in acquisition mode, the lowest noise floor (mean value $0.800\pm 0.004$, SNR 1.25) is obtained using a DPC sensor clock frequency of 160 MHz. The highest increase in noise resulting in lowest SNR occurs when the SDM clocks the sensor dies at 140 MHz (noise mean value $0.839\pm 0.004$, SNR 1.192). The relative difference with respect to the noise floor measured for 160 MHz is 4.88%.

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As shown by the results in figure 13, the SDM successfully acquired PET data even with our firmware modifications with regard to different clocking distribution patterns by means of sensor die clock frequency and phase shifts. However, a change of the clock frequency at which the DPC sensor is operated requires us to revise sensor-specific parameter settings which are clock-frequency dependent if aiming to keep values with regard to absolute time. Moreover, the lower the operating frequency of the sensor die, the higher the dead-time properties of the sensor. Dead-time in this context does not only refer to the amount of time needed to be able to successfully detect two successive scintillation events. It also covers the DPC sensor's bandwidth limitation, which decreases with decreasing operating frequency. The frequency dependence is related to the digital, clocked logic of the main acquisition controller of the DPC sensor (Frach et al 2009, 2010). The deterministic behaviour of the finite state machines in the acquisition controller, on the other hand, allows us to predict the frequency-dependent maximum bandwidth limitation per DPC sensor and thus the count rate limitations by calculations and simulations. Summarised, it can be derived that an MRI noise reduction obtained via PET-data-acquisition-related frequency adaptations may result in a trade-off between the gained noise reduction on one hand and the PET detector dead-time on the other hand, provided that the frequency adaptations affect clock domains such as the dSiPM operation or digital hardware- and firmware-based PET data acquisition.

Since RF resonators are designed to have characteristic resonance spectra (figure 4), the EM field coupling efficiency between a resonator and EM field transmitters strongly depends on the frequency of the field generated by external sources. As the spectrum measurements in figure 14(a) demonstrate, the spectrum of the EM field emission can be successfully altered by frequency modifications of the sensor die clock signal. Clock frequencies which fall within the bandwidth to which the MRI receive chain is sensitive will inevitably lead to a strongly increased noise floor due to the high amplitudes of the first harmonics of the periodic clock signal. This was demonstrated for the clock frequency of 127.78 MHz in figures 14(a) and 18(a). In addition to distinct amplitude peaks visible in the measured broadband spectra, a noise floor covering a continuous frequency range (in the frequency domain) is usually a result of an overlap of many EM field sources such as non-periodic electrical signal changes in components as well as PCB traces and connectors. The spectrum measured during SDM operation with a DPC sensor frequency of 140 MHz serves as a good example to demonstrate that, although this frequency does not fall directly within the MRI acquisition bandwidth ($128~\text{MHz}\pm 500$ kHz when performing noise scans), this clock frequency leads to a considerable noise floor rise around the Larmor frequency at 3 T, as visualised by the green plot in figures 14(a) and (b). This noise floor increase may be caused by non-periodic-data-line-switching-related field emission, whose spectra are influenced by the choice of the sensor die clock frequency while overlapping with RF fields originating from electronics not affected in their radiation behaviour by the sensor die clock frequency. Choosing a suitable clock frequency to lower the amplitudes of irradiated spectra within the MRI-sensitive bandwidth is therefore not trivial and in the end requires us to make spectrum measurements with analyser equipment and spurious noise measurements with the MRI and the desired RF coil setup. Our results obtained with frequencies of 100 MHz and 160 MHz clearly demonstrate that well chosen frequencies help to reduce PET-related RF noise, or in other words increase the RF silence of our PET detector.

The low MRI SNR obtained with the MR sequence is visible in the reference scan shown in figure 19(a). Counts detected by the SDM were created by low LYSO background radiation and dark counts related to thermal excitation. Except for the singles measurements, this corresponds to the measurement conditions in the laboratory and for the MR noise scans where no radioactive source was used. Placing a source in the vicinity of the SDM to change signal switching behaviour due to increased PET data message transmission between the stack and the SPU FPGAs may modify the RF field emission in such a way that the noise coupling is increased to further illustrate differences in MRI SNR deterioration at a higher order of magnitude depending on the chosen clock frequency. This, however, was not possible as no radioactive sources were allowed in the MRI facility where the SNR measurements took place. Nevertheless, the lower noise floor measured with an SDM operating with a clock frequency of 160 MHz compared to one with 140 MHz demonstrates that clock frequency adjustments of digital circuits can reduce the noise coupled into the RF coil. We expect the differences in terms of visual artefacts in MR images for a broader range of sequences to be more pronounced for the case of a measurement setup scaled up to ten SDMs (a complete PET insert) and using a coil such as a birdcage rabbit coil (presented in Weissler et al (2015a)) located closer to the PET detector than the mouse coil.

Our FEM simulations demonstrated that field pattern modifications can principally result in a reduction of RF field coupling into a RF resonator. These modifications were implemented and tested with an SDM by adapting the DPC sensor clock in-phase pattern to a checkerboard-phase pattern at SDM level. Comparing the characterised field emission maps depicted in figures 15 and 16 yields the conclusion that the emitted field distribution was modified upon a change of the clock phase pattern. In particular, the comparison of the top plane (which is oriented towards the PET module) measurements shows shifted peaks with similar peak amplitudes. Based on the simulation result, this alteration of the emitted field pattern is expected to change the coupling coefficient to the RF coil and thus is expected to show a different spurious signal (noise) production. This is indeed the case, as shown by the MRI noise measurements (figure 18).