PLoS ONEplosplosonePLOS ONE1932-6203Public Library of ScienceSan Francisco, CA USA10.1371/journal.pone.0237494PONE-D-19-28452Research ArticleMedicine and health sciencesDiagnostic medicineDiagnostic radiologyMagnetic resonance imagingResearch and analysis methodsImaging techniquesDiagnostic radiologyMagnetic resonance imagingMedicine and health sciencesRadiology and imagingDiagnostic radiologyMagnetic resonance imagingPhysical sciencesMathematicsOptimizationPhysical sciencesMathematicsApplied mathematicsAlgorithmsResearch and analysis methodsSimulation and modelingAlgorithmsPhysical sciencesPhysicsNuclear physicsNucleonsProtonsEngineering and technologyElectrical engineeringElectrical circuitsPhysical sciencesMathematicsApplied mathematicsAlgorithmsEvolutionary algorithmsResearch and analysis methodsSimulation and modelingAlgorithmsEvolutionary algorithmsResearch and analysis methodsComputational techniquesEvolutionary computationEvolutionary algorithmsEngineering and technologyTechnology developmentPrototypesResearch and analysis methodsImaging techniquesOptimization of high-channel count, switch matrices for multinuclear, high-field MRIHigh-channel count multinuclear switch matrix designhttp://orcid.org/0000-0001-6431-4322FelderJörgConceptualizationInvestigationMethodologyProject administrationSoftwareSupervisionVisualizationWriting – original draft1*http://orcid.org/0000-0003-3569-0905ChoiChang-HoonConceptualizationInvestigationWriting – original draft1KoYunkyoungInvestigationValidation1ShahN. JonConceptualizationSupervisionWriting – original draft1234Institute of Neuroscience and Medicine -4, Forschungszentrum Jülich, Jülich, GermanyInstitute of Neuroscience and Medicine -11, Forschungszentrum Jülich, Jülich, GermanyJARA—BRAIN—Translational Medicine, Aachen, GermanyDepartment of Neurology, RWTH Aachen University, Aachen, GermanyDenizCem M.EditorNew York University Langone Health, UNITED STATES
NJS and JF are co-founders of Affinity Imaging GmbH a spin-off company that manufactures high field MRI coils for research purposes. This does not alter our adherence to PLOS ONE policies on sharing data and materials.
* E-mail: j.felder@fz-juelich.de17820202020158e02374941110201928720202020Felder et alThis is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.
Modern magnetic resonance imaging systems are equipped with a large number of receive connectors in order to optimally support a large field-of-view and/or high acceleration in parallel imaging using high-channel count, phased array coils. Given that the MR system is equipped with a limited number of digitizing receivers and in order to support operation of multinuclear coil arrays, these connectors need to be flexibly routed to the receiver outside the RF shielded examination room. However, for a number of practical, economic and safety reasons, it is better to only route a subset of the connectors. This is usually accomplished with the use of switch matrices. These exist in a variety of topologies and differ in routing flexibility and technological implementation. A highly flexible implementation is a crossbar topology that allows to any one input to be routed to any one output and can use single PIN diodes as active elements. However, in this configuration, long open-ended transmission lines can potentially remain connected to the signal path leading to high transmission losses. Thus, especially for high-field systems compensation mechanisms are required to remove the effects of open-ended transmission line stubs. The selection of a limited number of lumped element reactance values to compensate for the for the effect of transmission line stubs in large-scale switch matrices capable of supporting multi-nuclear operation is non-trivial and is a combinatorial problem of high order. Here, we demonstrate the use of metaheuristic approaches to optimize the circuit design of these matrices that additionally carry out the optimization of distances between the parallel transmission lines. For a matrix with 128 inputs and 64 outputs a realization is proposed that displays a worst-case insertion loss of 3.8 dB.
The author(s) received no specific funding for this work.Data AvailabilityAll relevant data are within the manuscript and its Supporting Information files. We have also uploaded all source code of the project on the public Gitlab repository of the Research Center Jülich where it is freely available (https://gitlab.fz-juelich.de/j.felder/multinuclear-switch-matrix).Introduction
Modern magnetic resonance imaging (MRI) systems rely heavily on parallel imaging techniques using multi-channel, phased array coils. Currently, they are routinely employed to improve image quality, to reduce the scan time or to obtain more information (e.g. in multi-nuclear or multi-parametric measurements) within a given time frame. Moreover, reducing the scan time brings about further benefits in terms of increasing patient compliance (shorter scan times are more comfortable for the patient) and enables an increased workload of expensive MRI machinery (patient throughput can be increased). In fact, several applications would not be feasible at all without parallel imaging techniques. These include, but are not limited to, imaging the beating heart [1, 2], fast functional/diffusion imaging [3–7] and correcting unwanted artifacts, e.g. aliasing and ghosting [8, 9].
With the increase in the number of elements in phased array coils [10–12], more and more parallel receive channels are required per MRI system. Unfortunately, this has a significant negative impact in terms of machine cost due to the requirement for additional receiver units and a technologically complex patient table [13], on patient comfort and operator workflow arising from the bulky cable bundles on the local RF coils [13], and on the large amounts of data that require handling prior to final image reconstruction. Thus, the number of receive antennas (coils)–or at least the number of physical connection points in the patient table [14]–present in an MRI examination frequently exceeds the number of receivers available in the system. The problem is aggravated when large fields-of-view are to be covered and multiple coil arrays are used during a scan, e.g. in spine imaging and moving table acquisitions.
An early commercial solution to the problem was the incorporation of mode matrices in the receiver coil array [15]. These make use of the fact that the majority of the receive signal’s power is contained in a small number of RF modes. The concept can be compared to the use of circular polarized receive coils which employ two quadrature coil elements and combines these into a single receive signal. Thus, high-channel-count coil systems can be connected to fewer receiver channels, while avoiding significant penalties in the receive signal-to-noise ratio (SNR). However, the mode matrix approach significantly reduces the available acceleration factor for a given number of receive elements as it actually reduces the physical number of receive elements [16]. This factor is particularly significant in high-field systems, which are increasing in availability, as they potentially allow higher speed-up factors [17]. Thus, most modern MRI scanners have a large number of physical coil connectors distributed on the patient table that need to be flexibility connected to the available receivers with the established routing depending on the coils selected for the desired imaging task e.g. when full body coverage is desired [14] or multiple different type of local coils are employed in a single imaging session [13].
Signal routing from the physical coil connectors commonly located on the patient table to the receivers located in the technical room outside the Faraday shield in clinical MRI systems is usually achieved by using a module termed either the “switch matrix” (a term originally used in telecommunications and computer communication networks (e.g. [18] or “matrix switch” (e.g. [19]. The switch matrix is commonly located close to the magnet to avoid long coaxial cable bundles but physically behind the initial low noise preamplifier in order to maintain the highest possible SNR. A large number of implementations are feasible and can generally be categorized as crossbar switches or multiplex matrix switches [20]. Both of these, as well as hybrid topologies, have been used in MRI applications [21, 22]. Crossbar switch matrix implementations can either be achieved with the use of integrated circuits configured as single-pole double-throw (SPDT) switches, e.g. based on GaAs, GaN [23], or MEMS [24] switches, or by employing simpler single-pole single-throw (SPST) configurations, e.g. by using PIN-diodes. While the former implementation seems to be technologically more robust, as it allows to disconnect the remaining transmission line length from the active signal path and therefore does not contain remaining physically connected open-ended transmission lines, it requires the receive signal to pass through a high number of active switches. This potentially leads to high signal attenuation. As an example, a well-designed GaAs IC with suitably high linear power handling capability for MRI receive signals easily displays an insertion loss of 0.35 dB (e.g. SKY13351-378LF–Skyworks Solutions, Inc., USA). The receive signal has to cross this device (M-1) x N times in the worst case with M being the number of input lines and N the number of output lines.
Recently, PIN-diode controlled switch matrices have been shown to be feasible even in high-field MRI applications by either compensating open transmission line impedances with suitable lumped element terminations in one direction [25] or in both directions [26]. In addition, a method to reduce the PCB footprint for large size matrices using a combination of switch types has been presented [27].
To date, switch matrix design has mostly been concerned with routing the signals of the proton Larmor frequency as the number of available high receive channel arrays operating at non-proton frequencies at clinical field strength is limited to research coil implementations, e.g. [28, 29]. However, the routing of X-nuclei (non-proton, resonating at different frequencies) signals might still be required if the coil connectors on the patient table do not provide dedicated plugs for the X-nucleus’ receive coil arrays.
A number of switch matrix implementations with variable degrees of flexibility in routing configuration have been described in the literature: sparse or cascaded matrix designs are described in [13, 30, 31] and a full switch matrix is described in [32]. While they are routinely employed in MRI scanners operating at clinical field strength of 1.5 T and 3 T, in some commercial 9.4 T and 7 T systems, the switch matrix was removed and the signal was routed directly without the possibility to switch it to different receiver units. However, with the increased availability of high-field scanners, the benefits of X-nuclei imaging is likely to attract increased interest [33, 34]. As multichannel, X-nucleus coil arrays also provide improved SNR compared to volume coils, as is also the case in proton imaging, there is compelling motivation to also use coil arrays in these SNR-starved applications. In fact, multichannel X-nucleus arrays have been under active development for a number of years, and one can compare exemplary implementations in [35, 36] or [37] for a review on the topic. In this context, designing a switch matrix suitable for operation with protons and the most common X-nuclei at high-field is desirable. It would, for example, enable the combined operation of a CP mode proton coil with a 32-channel sodium array in a system equipped with 32 receive channels or the connection of more advanced double-tuned arrays as described in [38]. Note, that switch matrix implementations operating at the proton frequency as well as at one or more X-nucleus frequency has been previously described in [39].
In this manuscript we present a novel design methodology for a low-loss, high channel-count switch matrix based on SPST switches employing PIN diodes [26] capable of operating at, for example, 400 MHz (proton - 1H), 376 MHz (Fluorine - 19F), 162 MHz (Phosphorus - 31P), 106 MHz (Sodium - 23Na) and 54 MHz (Oxygen - 17O), these being the resonance frequencies of the said nuclei on a 9.4 T MR system. The method is based on multi-parameter optimization strategies and uses analytical transmission line formulas to derive optimum transmission line spacing and compensation elements on both horizontal and vertical switch matrix transmission lines.
Methods
Fig 1 shows the topology of a switch matrix employing a single PIN-diode at each junction. Note that single PIN-diode switches can make a connection between an input and an output, but cannot break it–they are acting in a SPST manner. Therefore, the transmission line stubs remain electrically connected. Thus, attenuation of the signal occurs, with the level of attenuation depending on the impedance transformation of the open transmission line to the location where the PIN-diode connects upper and lower transmission lines. The remaining vertical and horizontal stub lines will contribute to the signal attenuation across the switch matrix as described in [26].
10.1371/journal.pone.0237494.g001
Topology of a crossbar switch matrix (top) and prototype board (bottom). The top image shows an M-input x N-output freely configurable crossbar switch matrix using SPST switches. Selectable compensation elements, e.g. one capacitor and one inductor are located at the end of each transmission line stub. The SPST switches can be realized as a single PIN diode. The bottom images show the prototype PCB as well as the prototype connected to a birdcage coil including preamplifier and transmit/receive switch.
In order to demonstrate the implementation challenges, the attenuation arising from the unterminated transmission lines for a low channel-count (5 inputs x 5 outputs) switch matrix has been measured on a prototype board [26] for the connections shown in color in Fig 2 for a number of nuclei frequently used in high field MRI. Even for the small-sized matrix, the task of determining suitable compensation elements is tedious and evaluation of optimal compensation element values quickly becomes infeasible. Thus, for the sake of simplicity, Fig 2 reports results obtained for a single compensation element of 91 pF. In this prototype “switching” from unterminated to terminated stub lines was accomplished by soldering the termination impedance on the PCB. Only a limited number of switch matrix configurations with different stub line lengths were evaluated experimentally in order to demonstrate the negative influence of unterminated transmission lines on the IL per se. In a product implementation connection of the designated termination resistance will be implemented via SPST PIN diode switches.
10.1371/journal.pone.0237494.g002
Signal routes (colored) evaluated at different frequencies (left) and insertion loss measured on the bench for the different nuclei considered here. If the insertion loss was above 2 dB, a single value compensation (91 pF) was attached at one or both transmission lines and the insertion loss re-measured for all possible combination of compensation elements. All values are in dB; all input lines are designated as “Input” and all output lines as “Channel” with consecutive numbering. Transmission line stubs are labeled with alphabetical capital letters A to J. For the sake of clarity, only a limited number of matrix configurations have been evaluated experimentally, e.g. the switch was configured with fixed connections from input #1 to output #5, input #2 to output #4 and so forth to demonstrate the effect of transmission line stubs of different length for different resonant frequencies. In the table on the right, the value for the insertion loss shown in black indicates values measured for the unterminated case (that is, without the 91 pF attached to the transmission line stub). Red values are the ones representing IL for the terminated case (where the 91 pF are connected to the transmission line stubs). For the terminated case, the location of the termination capacitance is given underneath the measured IL values.
The worst-case IL in the small laboratory sample matrix evaluated in Fig 2 is 24 dB in the uncompensated case, while it is only 1.94 dB for a connection from input #1 to output channel #5 on the proton frequency when compensation elements are employed. To investigate the influence of IL on SNR and in order to establish the requirements for the circuit, optimization experiments were carried out on a 9.4 T animal scanner [40] by inserting a variable attenuator at the location of the proposed switch matrix. Single slice gradient echo (TE = 10 ms, TR = 100 ms, FA = 15) images were acquired using a linear-polarized birdcage resonator and a 63 ml sample (per 1000 g distilled water 5 g NaCl and 1.25 g NiSo4 x 6 H2O) to measure SNR as a function of attenuation as described in [41], Method 2. The results of the measurement are given in Fig 3.
10.1371/journal.pone.0237494.g003
Measured SNR of a GRE image versus signal attenuation at the position of the proposed switch matrix measured at 9.4 T.
MR images were acquired with a linear polarized birdcage and SNR was computed according to Method 2 described in [41].
The influence of signal attenuation on image quality for multiple nuclei was evaluated experimentally on the same NR system using an interchangeable set of quadrature birdcage coils with integrated transmit/receive switches and preamplifiers [42] and the prototype switch matrix shown in Fig 1 placed behind the coil connectors. Imaging of a phantom (50 ml cylindrical tube filled with doped water and 150 mM NaF (Sigma-Aldrich, German)) was carried out using the FLASH sequence at the 1H, 19F and 23Na frequencies. The sequence parameters were TE/TR = 3.95 ms/150 ms, FoV = 52x52 mm2, Matrix size 256x256, slice thickness 0.2 mm with a total acquisition time of 38.4 ms for the proton experiments, TE/TR = 2.48 ms/450 ms, FoV = 42x42 mm2, Matrix size 42x42, slice thickness 1 mm, flip angle 75°, 16 averages with a total acquisition time of 5 minutes for 19F, and TE/TR = 2.85 ms/40 ms, FoV = 30x50 mm2, Matrix size 30x50, slice thickness 1 mm, flip angle 60°, 16 averages with a total acquisition time of 2:34 minutes (3D) for 23Na. The images acquired with and without the terminating capacitances present are shown in Fig 4.
10.1371/journal.pone.0237494.g004
Measured FLASH images for different nuclei when the prototype switch matrix is present in the 9.4 T animal MR system.
The yellow text gives SNR values when leaving transmission lines uncompensated, the red text shows compensated (91 pF) transmission line stubs.
As can be seen from Figs 3 and 4, small values of attenuation already have a negative influence on the SNR of the image. Therefore, the switch matrix should be optimized for as low IL as possible. Consequently, for larger switch matrix sizes, which are likely to be encountered in the modern MRI systems, an algorithm is required that determines optimum compensation element values in an automated way. This optimization problem can use a single cost function (C) and minimizes the maximum insertion loss (IL) encountered for all switch configurations given that the optimum stub termination is selected for a given signal routing scheme. For a M x N switch matrix this is expressed as
C=max(IL(i,j,fk))∀i=1..M,j=1..N
with M and N being the number of input and output lines, respectively, and fk being the operating frequencies. Eq (1) is similar to using a weighted Tchebycheff model with weighting coefficients set to equal one as described in [43]. Due to the large number of variables equaling possible terminations for each stub line, metaheuristic approaches [44] are suitable for optimization of the switch matrix circuit. Metaheuristics can be classified as single solution approaches which act on a single candidate solution, e.g. simulated annealing [45] and variant local search methods, or population-based approaches [46]. The latter includes nature-inspired algorithms, such as evolutionary algorithms, particle swarm optimization [47], firefly algorithms [48] and artificial bee colonies [49]. While metaheuristic population-based approaches are not guaranteed to find the globally optimum solution, a recent comparison has shown that they are competitive with deterministic Lipschitz algorithms [50] in many respects. This, along with their relative ease of use, are the motivation for applying them to the switch matrix optimization for multi-nuclear, high-field MRI.
IL can be computed as the sum of the mismatch loss and transmission losses over the transmission lines used in the switch matrix, e.g. compare [51]. Mismatch loss is computed by first transforming the compensation impedance of the two stub lines to the active switch junction. This uses the impedance transformation formula for transmission lines of characteristic impedance Z0 terminated with the impedance ZL along the stub line length l
Zinput=Z0ZL+Z0tanhγlZ0+ZLtanhγl
with γ being the complex propagation constant of the transmission line [52].
At this point, the parallel impedance of the stub lines and the 50 Ohm load from the receiver are computed and further transformed to the switch matrix input. This enables the impedance, and hence the mismatch loss at this point, to be calculated.
The microstrip transmission lines used in the calculations have been designed to display a characteristic impedance of 50 Ohms when built on an FR4 substrate with a thickness of 1.5 mm (relative dielectric constant εr = 4.6, copper trace thickness t = 0.035 mm, substrate thickness h = 1.5 mm, microstrip trace width w = 2.725 mm, loss tangent of substrate tan δ = 0.022, surface roughness–rms deviation of the conductor surface from a plane–Rough = 0.055, and relative conductivity with respect to copper Rho = 1). The transmission line parameters were calculated online (http://mcalc.sourceforge.net) using a method which employs the formulae derived by Hammerstad and Jensen [53] and is conveniently summarized in e.g. [54].
Implementation of circuit optimization
Circuit optimization was carried out with Python [55] using the platypus package [56]. The cost function is implemented in two subroutines–one computing the optimum termination and returning minimal insertion loss for a single switch junction, while the outer subroutine computes the maximum insertion loss over all junctions. The cost function is parameterized so as to allow the maximal insertion loss for a number of operating frequencies to be found, as well as having the choice to place more than one compensation element per transmission line stub. It should be noted that the range of termination elements allowed was limited from 300 nH inductive to 200 pF capacitive, which covers available lumped, high-frequency elements with suitable self-resonances and quality factors. This range was also mapped onto a real valued space, between +1 and -1 for equidistant gridding during program execution to ensure that standardized initialization of the search space remained feasible. The final goal of the study was to design a multi-nuclear switch matrix with 128x64 channels. The dimensions were selected according to the maximum number of receiver channels available in commercial 7 T systems and the maximum number of receive elements in an experimental coil array described so far [57].I Initial investigations of algorithm performance were carried out on differently sized matrices for the sake of simplicity.
In an initial evaluation, several multi-objective optimization algorithms based on evolution strategies—a variant of evolutionary computing which is inspired by acting upon populations underlying variation and selection in generational loops [58]–were compared in order to evaluate their performance for the switch matrix optimization task. This was done for a 64x32 sized matrix operating at the proton frequency of 400 MHz and allowing two compensation elements for each stub. For this investigation, the transmission lines were assumed to be lossless. The strategies investigated were: a non-dominated sorting genetic algorithm II (NSGA-II) [59] and its more recent version NSGA-III [60], a covariance matrix adaptation evolution strategy (CMA-ES) [61], a generalized differential evolution (GDE3) [62], an indicator-based evolutionary algorithm (IBEA) [63], a multi-objective evolutionary algorithm based on decomposition (MOEA/D) [64], a multi-objective (OMOPSO) [65] and speed-constrained multi-objective particle swarm optimizer (SMPSO) [66], a strength Pareto evolutionary algorithm (SPEA2) [67] and an epsilon multi-objective evolutionary algorithm (ε-MOEA) [68]. In addition to using different optimization methods, the strategies employed also differ in their approaches to evaluating the Pareto optimality of the population. For example, the NSGA derivatives employ dominance depth, while SPEA uses dominance count/rank; a different approach is to use performance measures for the selection step, e.g. in IBEA [43]. For an in-depth discussion of the properties of the different algorithms, the reader is referred to standard textbooks, e.g. [43]. A list of active projects implementing multi-objective optimization in the Python programming language is given in [69]. All algorithms were executed with 10 random seeds and ran for a maximum of 2000 iterations.
Using the optimization algorithm selected during the initial evaluation, a multi-nuclear switch matrix with 16 inputs and 8 outputs was designed for operation at the 1H, 19F, 31P, 23Na, and 17O Larmor frequencies of a 9.4 T system. This time, attenuation on the microstrip lines was accounted for by using a complex propagation constant for each frequency. In addition, a variable, but unique, spacing between neighboring transmission lines in the range 10 mm to 60 mm was considered during the optimization to allow the circuit geometry to be optimized in combination with the compensation elements. The lower limit was imposed so as to avoid closely spaced lines with high coupling between neighboring lines. Compensation elements were allowed from a maximum of 300 nH inductive to 200 pF capacitive, as above. This more realistic design example was evaluated with the three best-performing algorithms found during the initial comparison.
Finally, a large sized multi-nuclear matrix with 128 input lines and 64 output lines was optimized using the same constraints as given above. This time, only the ε-MOEA algorithm was investigated as it provided the best results for the two test cases investigated beforehand. The number of algorithm iterations was increased until no further improvement in the overall cost could be obtained.
Results
Table 1 shows the highest insertion loss for any path across a 64x32 sized matrix obtained from optimizing the compensation elements with the different algorithms. It can be seen that NSGA-II, SPEA and ε-MOEA performed best in this task, while other algorithms converged to significantly worse solutions, despite being executed for a number of seed values.
10.1371/journal.pone.0237494.t001
Highest insertion loss (IL) obtained for any switch configuration for a 64x32 sized, proton only matrix when neglecting transmission line losses.
Optimization Algorithm
Highest IL for any signal path [dB]
NSGA-II
1.198
NSGA-III
6.884
CMA-ES
4.335
GDE3
5.041
IBEA
1.205
MOEAD
12.278
OMOPSO
3.617
SMPSO
2.109
SPEA
1.208
ε-MOEA
1.140
The three algorithms that converged to an insertion loss below around 1.2 dB were further evaluated on a more realistic multi-nuclear switch design task. This task was based on a 16 x 8 switch matrix and the insertion losses for each nucleus and each switch configuration are shown in S1 to S3 Figs. The overall results for the optimization with a maximum number of algorithm executions of 4000 times are given in Table 2.
10.1371/journal.pone.0237494.t002
Overall performance of the optimization algorithms for the 32 x 16 multi-nuclear switch matrix design (IL–insertion loss, TL–transmission line).
NSGA-II
SPEA2
ε-MOEA
Highest IL: 1.20 dB
Highest IL: 1.31 dB
Highest IL: 1.00 dB
Vert. TL distance: 10.2 mm
Vert. TL distance: 18.5 mm
Vert. TL distance: 10.7 mm
Hor. TL distance: 12.4 mm
Hor. TL distance: 10.9 mm
Hor. TL distance: 10.2 mm
Execution time: 263 s
Execution time: 335 s
Execution time: 1054 s
The results for the full-sized switch matrix (128 x 64 ports) designed with ε-MOEA are given in Fig 5. Table 3 provides a detailed performance evaluation for different numbers of algorithm execution.
10.1371/journal.pone.0237494.g005
Maximum IL for the full switch matrix size for all nuclei investigated as obtained with the ε-MOEA algorithm.
For better visibility, the switch matrix was rotated so that the output ports are shown on the left-hand side (abscissa) ranging from 1 (top) to 64 (bottom). The inputs are arranged along the ordinate and increase from right to left. Each color patch gives the maximum IL for the connection between the corresponding input and output port. All data are simulation results calculated using the transmission line formulas from Hammerstad et al. [53].
10.1371/journal.pone.0237494.t003
Performance as a function of the number of algorithm executions for the full-sized matrix design.
N = 2000
N = 4000
N = 8000
N = 16000
Highest IL: 5.06 dB
Highest IL: 4.25 dB
Highest IL: 3.84 dB
Highest IL: 3.81 dB
Vert. TL dist.: 11.2 mm
Vert. TL dist.: 10.4 mm
Vert. TL dist.: 10.0 mm
Vert. TL dist.: 10.0 mm
Hor. TL dist.: 23.3 mm
Hor. TL dist.: 13.0 mm
Hor. TL dist.: 10.2 mm
Hor. TL dist.: 10.4 mm
For the 128x64 matrix, a maximum IL over all nuclei of 3.81 dB was encountered. Horizontal and vertical transmission lines were spaced at 10.0 mm and 10.4 mm, respectively. Thus, the maximum transmission line length was approximately 1885 mm (123 x 10.0 mm + 63 x 10.4 mm), resulting in an attenuation of 3.28 dB at the proton frequency along the line. The high losses attributed to attenuation along the transmission lines become clearly visible in the lower-left corner (corresponding to the longest path of the switch matrix) of the 1H and 19F attenuation maps shown in Fig 5. The mean insertion losses and standard deviations of the optimized matrix were 2.38 dB ± 0.86 dB, 2.26 dB ± 0.81 dB, 1.19 dB ± 0.44 dB, 0.90 dB ± 0.36 dB and 0.63 dB ± 0.39 dB for the 1H, 19F, 31P, 23Na and 17O frequencies, respectively.
Discussion
We have shown that SNRs of both, proton and X-nucleus signals can be significantly affected when using a switch matrix to route receive signals from the coil connectors on the patient table to the receivers of an MR system. Thus, suitable circuit topologies that reduce signal attenuation in the switch matrix as much as possible are required. In this manuscript we demonstrate that circuit optimization of a large, multi-nuclear switch matrix is feasible even when using a limited number of compensation elements to compensate for the influence of open-ended transmission lines of varying length. Optimization, although using a single cost function only, was carried out with a variety of multi-objective optimization strategies which employ either swarm like features or genetic principles and are thus suitable candidates for metaheuristic, non-convex problems. The non-convexity of the optimization problem at hand arises from the magnitude operation in the IL formulation. These algorithms have been employed successfully in other fields of MRI, e.g. for B1 shimming [70] using different single cost functions and a particle swarm approach and in coil circuit optimization [71] with three optimization targets and employing CMA-ES. In the presented optimization task, the optimization was able to generate a circuit topology that caused an addition IL of only 0.6 dB above that of the attenuation of the longest transmission line. With a maximum overall IL of below 4 dB, the degradation in image SNR is negligible, as we demonstrated with attenuation measurements on a 9.4 T scanner.
In our investigation, we found ε-MOEA to perform best out of the tested candidate algorithms. While this is a lesser-known evolution strategy [72] and was shown to be less performant in an biobjective testbed [73] it consistently outperformed the other algorithms implemented in the platypus collection. The good performance of the ε-MOEA algorithm might be due to the fact that, in contrast to generational algorithms which evolve the entire population at every iteration, ε-dominance archives ensure convergence and diversity throughout search for a proper selection of the ε parameter [74]. However, further investigation is required to back up this hypothesis.
From initial tests using multiple cost functions–single cost functions for all switch matrix junctions–it quickly became evident that one combined target function performed superior. This is in line with [70], where the formulation of multiple optimization goals was found to be feasible but was not chosen in the final implementation. The number of algorithm executions for the optimization to converge of around 16,000 is in the range reported in [50]. While the metaheuristic approaches employed are not guaranteed to converge to the global optimum, a comparison with the IL on the longest transmission line arising from attenuation only lends reasonable credit only to the results obtained with the proposed optimization strategy.
It should be noted, therefore, that for the investigations presented here, no experimental validation has been carried out for the full-scale matrix, since the intention was solely to investigate a feasible solution of the given optimization problem. However, from the investigations carried out in prior work [26, 27], we feel that agreement between simulation and measurement has been sufficiently demonstrated. Further validation is given in S4 Fig which compares IL for a 6x3 matrix optimized with the proposed algorithm with those obtained from a circuit simulator. The impact on of insufficient transmission line compensation on MRI image quality has been investigated both previously and in this work and allows a compromise between the envisaged switch matrix implementation and the associated image degradation to be found.
While this work focuses on the classical topology of a PIN-diode based switch matrix, which results in a rather large PCB footprint–e.g. the 128 x 64 switch matrix designed in this work measures approximately 1250 mm x 660 mm–the workflow can be used in combination with alternative matrix implementations. One possibility could, for example, be to use the switch matrix designed in this work to optimize the sub-matrices presented in [27] for stacked matrix designs or to reduce the flexibility of the switch matrix by using a multiplexer circuit that combines a number of input lines prior to routing through the switch matrix, e.g. as suggested in [21, 25]. It is certainly also feasible to change the number of allowed compensation elements, e.g. using a single termination only as described previously or to increase the number of elements to three to decrease the maximum IL further.
Supporting information
Maximum IL for all switch configurations for all nuclei investigated as obtained with the NSGA-II algorithm for a 16x8 sized matrix.
Note that the optimum termination for each case is given in the respective field for the vertical line (top row) and horizontal line (bottom row).
(PNG)
Maximum IL for all switch configurations for all nuclei investigated as obtained with the SPEA2 algorithm for a 16x8 sized matrix.
(PNG)
Maximum IL for all switch configurations for all nuclei investigated as obtained with the ε-MOEA algorithm for a 16x8 sized matrix.
(PNG)
Comparison of IL computed with the proposed method and obtained by circuit simulation using the free software package QUCS (available from qucs.sourceforge.net).
Both plots are normalized with respect to their maximum IL in color coding. While the pattern looks similar the circuit simulator predicts slightly larger insertion losses in all cases, which is probably due to using slightly different formulae for calculating transmission line properties.
(PNG)
The authors would like to thank the reviewers of [26] for bringing the idea of circuit optimization for large-scaled switch matrices to the attention of the authors. We sincerely hope that this work does justice to the questions raised during the review process. We thank C. Rick for careful proof reading of this manuscript.
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Combining Convergence and Diversity in Evolutionary Multiobjective Optimization. . 2002;10(3):263–82. doi: 10.1162/1063656027602341081222799610.1371/journal.pone.0237494.r001Decision Letter 0DenizCem M.Academic Editor2020Cem M. DenizThis is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.Submission Version0
13 Feb 2020
PONE-D-19-28452
Optimization of high-channel count, switch matrices for multinuclear, high-field MRI
PLOS ONE
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Your manuscript was reviewed by three experts in MRI system and coil design. All the reviewers identified that the study needs to be substantially improved in order to meet publication standards. Specifically, R1 requested you to incorporate more details of the method in the current manuscript. R2 suggested you demonstrate how does proposed switch matrices translate to MR image quality, and to extend the methods section to explain design parameters clearly. R3 suggested you improve the introduction by stating the motivation behind the work and identifying the problems of existing switches explicitly. As highlighted by the reviewers, I suggest you validate the simulations by providing an experimental proof-of-concept study as referencing to prior work (Ref. 19-20) would not be sufficient. In addition, the image quality of all figures needs to be improved. In the view of reviews and my assessment of the manuscript, I recommended a major revision to give you enough time to prepare the revised manuscript improved by a proof-of-concept study.
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Reviewer #1: This research paper provides a method of directly evaluating the loss in switch matrices used in receive arrays for different nuclei at 9.4T and compares different algorithms for finding terminations that minimize the insertion loss in the switching. The authors have very clearly outlined their process and detailed the results, while showing that significant improvements are obtained by the method. There is not enough details provided, and I am not specifically well informed enough, to determine if there are any issues with the implementation with the algorithms or if there was an expected result for the comparison of the different algorithms based on previous studies.
There are a number of specific comments on details and changes that can be made to improve the paper:
Page 3, line 55 – change “speed up” to acceleration factor
Page 4, line 80 – this phrasing makes it seem like multinuclear arrays are a new development, and the quotes reference is not a very early or specifically monumental reference of a multinuclear array. Please find more relevant and primary references and describe the development of X-nuclei array more fully.
Page 5, line 96 – replace “Note also that, both” with “The”
Figure 1- it may be the output settings for this pdf, but the figures are almost illegible, thus for publication will be necessary to make sure they are all of high quality
Figure 2- this graph/figure does well to highlight the importance of modifying the resulting stubs to avoid insertion losses that would degrade noise factor However it also seems to provide evidence that a more complicated approach is not needed, as the maximum loss of 2.21dB would have very little effect on the final noise figure considering the gain of the preamplifier stage.
The author’s previous publication “Signal Loss Compensation of RF Crossbar Switch Matrix System in Ultra-High Field MRI” also seems to point to this conclusion. This particular point should be addressed more explicitly.
Some rough estimate of at what point the losses may result in an SNR loss of perhaps >5% and 2% for a single channel would be valuable.
Page 8, line 175- add comma: “This time,”
Figures 3-5 do not provide much interesting information as there is no way to know from the text or discussion of the algorithm why specific switch combinations had lower insertion loss compared to others. However, there’s some value in seeing the difference with all the different nuclei at once. I suggest that this figure may only need to be shown for one algorithm, and then it can be detailed what specific differences the different algorithms had. Right now, it is not detailed why any specific differences are observed.
For this provided manuscript these figures 3-5 are also illegible
Page 12,line247- It would greatly enhance the work if some detailed explanation and discussion of why the �-MOEA algorithm performed best and where and why the other algorithms found non-optimal solutions. As this is the best performing algorithm it would also be best to detail it more explicitly in the methods.
Page 12,line256- I would agree that for the particular problem investigated here the theoretically derived insertion losses for transmission lines should match very closely with experimental.
Page 12, Line 264- The 1250 mm x 660 mm size is very large, A reference or details on what is currently used in commercial systems should be included. Also, in should be discussed: how necessary is it that every channel is able to be mapped or switched between every output. I believe this specific set-up is actually not very applicable for this reason.
Discussion points: why the different algorithms had different execution times and some idea of how much this could change with optimization.
Some description in the methods, if possible, of the specific classes the algorithms fall under
More time needs to be spent formatting the references correctly and more consistently.
Reviewer #2: The authors present a novel design methodology for a broadband switch matrix. Its frequency is ranging from 54 to 400 MHz. As it is seen in fig 1, it seems that its hardware does not require any novelty to make the design in broadband as the authors have published the design of the PIN-diode based switch matrix before (ref 19). The novelty in PIN-diode based switch matrix design is not clear in this manuscript. As the authors mentioned mostly in the introduction section on hardware design parameters, this manuscript is on various optimization algorithms employed to optimize the performance of the switch matric design. The choice of performance parameters demonstrated in this manuscript was not clearly explained in the methods section and its motivation was not clearly given in the introduction and discussion sections. The combination of design and optimization methods in the switch matrix was shown in the manuscript but its translation into the MRI image quality and image acquisition speed is missing in the manuscript.
In general, the used language in this manuscript is adequate but it contains a few grammatical errors. The relevant referencing was sometimes missing in the introduction. Unfortunately, the image quality of the figures in the pdf is very bad, so I have to ask to the authors to improve the quality of all figures in the manuscript. The tables require further explanations in the caption since the parameters and abbreviations were not included. My detailed comments and questions are attached in the pdf.
Reviewer #3: The authors compare several optimization methods for address the non-convex problem of optimizing RF PIN diode switch performance for MRI receive chains that have multi-nuclear capability. The authors show how adding a small number of discrete impedance elements to the end of stubs in a cross-bar switch network can greatly improve insertion loss by compensating for the variable lengths of stubs, which depend on which output a given input is connected to. The optimization method provides a design for 128 input ports and 64 output ports that works at several X-nuclei frequencies and provides maximum insertion losses that are at most 0.6 dB above the baseline loss for the transmission line in the switch itself. I think the strength of the paper lies in its comparison of several optimization methods that can handle non-convex objective functions, and in the comparatively simple switch network design that requires only four impedance options at the end of each stub to provide adequate degrees of freedom for achieving good impedance match across a variety of stub lengths and operating frequencies.
For general context, I think the authors should add a brief discussion in the introduction about how multi-nuclear signal reception is handled on existing ultra high field scanners that have X-nuclei capability. On these scanners you can choose which nucleus to measure on each receive channel on the patient table socket. Do the authors know what kind of switching hardware is used on these scanners? What about these existing switches is suboptimal? Too much insertion loss for certain configurations? A better discussion of the shortcomings of existing technology would help motivate the switch optimization framework described in the present manuscript.
In previous work the authors show some loss of image SNR due to transmission line losses (Ref. 19). How much does the switch insertion loss impact the final image SNR (and the total system noise figure)? The signals have already passed through a preamplifier, so subsequent losses have less impact on the overall noise figure of the system compared to losses at the coil itself before amplification.
Is there a closed-form expression for the insertion loss as a function of the stub lengths and termination impedances? This would be helpful for readers to see since it will provide more intuition for the optimization problem that is being solved. The authors reference “analytical transmission line formulas” but do not include them in the paper. Equation 1 is not particularly helpful by itself. I would include more detail here so that readers don't have to consult other publications to understand the objective function fully.
Some experimental results would help validate the proposed optimization framework. It would make the paper more convincing if the authors could show that a prototype switch circuit indeed works for all the multinuclear frequencies of interest with the predicted insertion loss in each channel. A small board (such as 5x5 channels) should be sufficient for proof of concept. This would significantly strengthen the manuscript. I don’t think actual NMR measurements are needed, just bench top validation using a network analyzer to verify that the predicted insertion loss at each frequency for each switch configuration matches the experimental results.
I would try to include more key results in the abstract. For example, what is the average insertion loss for a naive switch with no impedance compensation elements at the end of each stub, as compared to the optimized result that shows no more than 0.6 dB of added insertion loss above the basic transmission line losses.
3.28 dB of transmission line loss for the proton frequency seems quite high. Is a low-loss dielectric substrate used?
How will the switching between the different stub termination impedances be implemented in practice?
“In this context, designing a switch matrix suitable for operation with protons and the most common X-nuclei at high-field is desirable.” Can the authors clarify exactly what role the switch will play on a multi-nuclear scanner? For example using the same plug on the patient table to route different coil channels to different X-nucleus receiver channels inside the scanner.
Can the authors discuss why the problem is non-convex? What properties of the objective function make it non-convex?
I think it would be good to include more details about the circuit design from Ref. 19 for readers who don’t have time to consult that reference. For example, I found it helpful to look at Fig. 2c from Ref. 19. At a minimum, I would draw the PIN diode circuit symbol in at least one of the figures to show how it functions in a crossbar switch, to help readers appreciate why the stubs remain after an input is connected to a desired output channel.
Please expand caption for Figure 2 and add appropriate labels to figure. Explain explicitly what is meant by “Input 1, 2, 3…”, “Channel 1, 2, 3, …” and the letters “A, B, C, …”
Figure 1. Is “voltage controlled RF switch” the same as PIN diode switch? A PIN diode is really “current-controlled” since it requires current to be forward biased, so it might be more accurate to call it current-controlled or just a “PIN diode-actuated switch”.
Figure 2 caption. Please add more detail to the caption (and manuscript text), for example describing what is denoted with the red text and red outline. Also why aren’t the other switch cases considered, for example Input 1 going to Channels 1-4? Shouldn't all inputs be able to connect to all output channels? This is not clearly explained in the text. Are the values reported in Fig. 2 calculated or measured experimentally?
I would recommend adding more labels and details to Figures 3-5. Please add labels for the rows and columns of each matrix. And please add more detail to the caption explaining what is going on in the matrices/tables. I assume the two entries in each cell correspond to the selected impedance for the two stubs realized on the two sides of the PCB for minimizing the insertion loss. Same for Figure 6, please add labels to each panel in the figure. I assume the dimension of the arrays is 128x64? Please clarify that the values are simulated.
Is the 17O insertion loss generally lower than the other isotopes because of its lower Larmor frequency?
“…allowed was limited from 300 nH inductive to 200 pF capacitive, which covers available lumped, high frequency elements with suitable self-resonances and quality factors.” I assume these parts are non-magnetic and that this limits the readily available range of component values. Or were there other factors motivating the specific choice of impedance matching component values?
p. 7: “128x64 channels…” What does each dimension refer to? 128 inputs and 64 outputs?
Abstract
“…high field systems…”
“As multichannel X-nucleus coil arrays provide the same array SNR benefits as in proton imaging, there is compelling motivation to also use coil arrays in these SNR-starved applications.”
p. 4: “However, with the increased availability of ultra high field scanners, the benefits of X-nuclei (non-proton, resonating at different frequencies) imaging is likely to attract increased interest.”
p. 5: “…as previously described in Ref. (19) for the connections…”
p. 7: “tuple” is somewhat uncommon usage here.
p. 9: “…while other algorithms converged to significantly worse solutions…”
p. 9: “This task was based on a…”
p. 12: “…lends reasonable credibility only to the results obtained…”
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Reviewer #1: Yes: Adam Maunder
Reviewer #2: No
Reviewer #3: Yes: Jason P. Stockmann
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Submitted filename: review_P_2020.pdf
10.1371/journal.pone.0237494.r002Author response to Decision Letter 0Submission Version1
28 May 2020
All responses to reviewer and editor comments are uploaded as a separate file.
Submitted filename: Respose_To_Reviewers.docx
10.1371/journal.pone.0237494.r003Decision Letter 1DenizCem M.Academic Editor2020Cem M. DenizThis is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.Submission Version1
20 Jul 2020
PONE-D-19-28452R1
Optimization of high-channel count, switch matrices for multinuclear, high-field MRI
PLOS ONE
Dear Dr. Felder,
Thank you for submitting your manuscript to PLOS ONE. After careful consideration, we feel that it has merit but does not fully meet PLOS ONE’s publication criteria as it currently stands. Therefore, we invite you to submit a revised version of the manuscript that addresses the points raised during the review process.
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We look forward to receiving your revised manuscript.
Kind regards,
Cem M. Deniz
Academic Editor
PLOS ONE
Additional Editor Comments (if provided):
Your manuscript received favorable feedback from reviewers. There are minor changes needs to be addressed as highlighted by Reviewers 1 and 3. Please prepare a revision addressing reviewers' suggestions.
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Reviewers' comments:
Reviewer's Responses to Questions
Comments to the Author
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Reviewer #1: All comments have been addressed
Reviewer #2: All comments have been addressed
Reviewer #3: All comments have been addressed
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2. Is the manuscript technically sound, and do the data support the conclusions?
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Reviewer #1: Yes
Reviewer #2: Yes
Reviewer #3: Yes
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Reviewer #1: Yes
Reviewer #2: Yes
Reviewer #3: Yes
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Reviewer #1: Yes
Reviewer #2: Yes
Reviewer #3: Yes
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Reviewer #1: Yes
Reviewer #2: Yes
Reviewer #3: Yes
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6. Review Comments to the Author
Please use the space provided to explain your answers to the questions above. You may also include additional comments for the author, including concerns about dual publication, research ethics, or publication ethics. (Please upload your review as an attachment if it exceeds 20,000 characters)
Reviewer #1: I think the manuscript has been significantly improved. The information provided, with the evaluation of loss in SNR with different nuclei with different attenuation, puts into context the improvements in IL with the switch matrices. The additional literature references on the algorithms and availability of the used algorithm provide a way to evaluate the success of the implementation here as well. The comments listed below can be corrected in editing and don’t require another review.
Minor Comments:
In abstract,
Instead of writing “For a matrix with 128 inputs and 64 outputs a realization is proposed that
displays a worst-case insertion loss of just 0.6 dB above that of the attenuation of the longest transmission line.”
Write
“For a matrix with 128 inputs and 64 outputs a realization is proposed that
displays a worst-case insertion loss of {the insertion loss}”
page 3, row 92: have defined “single-pole doublethrow (SPDT) twice”
The introduction has been improved greatly and reads very well, with a more than extensive review of the literature.
The introduction has been improved greatly and reads very well, with a more than extensive review of the literature.
Page 11, row 256: units for surface roughness are missing, also which is being quoted, peak-to-valley roughness (Rz), average roughness (Ra), or RMS roughness (Rrms)?
Reviewer #2: Thanks for addressing all questions and comments.
Reviewer #3: Supporting Figure 4 has no labels accompanying the table/matrix. A label or title would be helpful.
For a PIN diode switch to be effective, a good bias tee must be used to inject the bias current into the PIN diode path, while blocking RF from the DC bias path. What kind of choke is used that is effective for blocking all the X-nuclei frequencies? Typically an inductor with appropriate self-resonance frequency a little bit higher than the Larmor frequency is used, but for the case of a switch handling multiple Larmor frequencies, this is more complicated. An inductor with suitably high inductance might work decently for all the frequencies used, but this might require a ferrite component. Some basic design details might be helpful to other investigators wishing to reproduce the work (using non-magnetic circuit components).
The authors write on p. 6, line 122, that on some systems, including 7T systems, "the switch matrix was removed and the signal was routed directly without the possibility to switch it to a different receiver unit". I'm still confused about this. On the Siemens Magnetom 7T at my institution, the coil file specifies whether the pins on Plug 3 should be used for, say, 1H or 31P signal reception. There is presumably a switch somewhere in the receive chain to route the signals accordingly.
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Reviewer #1: Yes: Adam Maunder
Reviewer #2: Yes: Ozlem Ipek
Reviewer #3: Yes: Jason Stockmann
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While revising your submission, please upload your figure files to the Preflight Analysis and Conversion Engine (PACE) digital diagnostic tool, https://pacev2.apexcovantage.com/. PACE helps ensure that figures meet PLOS requirements. To use PACE, you must first register as a user. Registration is free. Then, login and navigate to the UPLOAD tab, where you will find detailed instructions on how to use the tool. If you encounter any issues or have any questions when using PACE, please email PLOS at figures@plos.org. Please note that Supporting Information files do not need this step.
10.1371/journal.pone.0237494.r004Author response to Decision Letter 1Submission Version2
27 Jul 2020
The detailed response to the reviewers' concerns has been uploaded as an additional file.
10.1371/journal.pone.0237494.r005Decision Letter 2DenizCem M.Academic Editor2020Cem M. DenizThis is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.Submission Version2
29 Jul 2020
Optimization of high-channel count, switch matrices for multinuclear, high-field MRI
PONE-D-19-28452R2
Dear Dr. Felder,
We’re pleased to inform you that your manuscript has been judged scientifically suitable for publication and will be formally accepted for publication once it meets all outstanding technical requirements.
Within one week, you’ll receive an e-mail detailing the required amendments. When these have been addressed, you’ll receive a formal acceptance letter and your manuscript will be scheduled for publication.
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Kind regards,
Cem M. Deniz
Academic Editor
PLOS ONE
Additional Editor Comments (optional):
Congratulations on the acceptance of your paper!
Reviewers' comments:
10.1371/journal.pone.0237494.r006Acceptance letterDenizCem M.Academic Editor2020Cem M. DenizThis is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.
5 Aug 2020
PONE-D-19-28452R2
Optimization of high-channel count, switch matrices for multinuclear, high-field MRI
Dear Dr. Felder:
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