Eddy Currents Probe Design for NDT Applications: A Review.

Eddy current testing (ECT) is a crucial non-destructive testing (NDT) technique extensively used across various industries to detect surface and sub-surface defects in conductive materials. This review explores the latest advancements and methodologies in the design of eddy current probes, emphasizing their application in diverse industrial contexts such as aerospace, automotive, energy, and electronics. It explores the fundamental principles of ECT, examining how eddy currents interact with material defects to provide valuable insights into material integrity. The integration of numerical simulations, particularly through the Finite Element Method (FEM), has emerged as a transformative approach, enabling the precise modeling of electromagnetic interactions and optimizing probe configurations. Innovative probe designs, including multiple coil configurations, have significantly enhanced defect detection capabilities. Despite these advancements, challenges remain, particularly in calibration and sensitivity to environmental conditions. This comprehensive overview highlights the evolving landscape of ECT probe design, aiming to provide researchers and practitioners with a detailed understanding of current trends in this dynamic field.

Alternating magnetic field guiding system for MNP hyperthermia treatment of deep-seated cancers.

OBJECTIVES: Demonstrate the potential application of a novel, endoscope-like device to guide and focus an alternating magnetic field (AMF) for treating deep-seated cancers via magnetic nanoparticle hyperthermia (MNPH). METHODS: AMF delivery, MNP activation, and eddy current distribution characteristics are investigated through experimental studies in phantoms and computational simulations using a full 3-dimensional human model. The 3D simulations compare the novel device to traditional AMF designs, including a MagForce-like, two-coil system (used clinically) and a single surface-coil system. RESULTS: The results demonstrate that this approach can deliver the same magnetic field strength at the prostate's centroid as traditional AMF designs, while reducing eddy current heating by 2 to 6 times. At the same level of normal tissue heating, this method provides 5.0 times, 1.5 times, and 0.92 times the magnetic field strength to the nearest, centroid, and farthest regions of the prostate, respectively. CONCLUSIONS: These results demonstrate proof-of-concept for an endoscopic magnetic field guiding and focusing system capable of delivering clinically relevant AMF from a distance. This innovative approach offers a promising alternative to conventional field delivery methods by directing AMF through the body, concentrating it in the tumor region, reducing eddy currents in surrounding healthy tissue, and avoiding exposure of nearby metallic implants.

Acoustic noise reduction in the NexGen 7 T scanner.

PURPOSE: Driven by the Lorentz force, acoustic noise may arguably be the next physiological challenge associated with ultra-high field MRI scanners and powerful gradient coils. This work consisted of isolating and mitigating the main sound pathway in the NexGen 7 T scanner equipped with the investigational Impulse head gradient coil. METHODS: Sound pressure level (SPL) measurements were performed with and without the RF coil to assess its acoustic impact. Vibration measurements were carried out on the gradient coil, the RF coil, and on the patient table to distinguish the different vibration mechanisms and pathways. Vibrations of the RF coil were modified by either making contact with the patient bore liner with padding material or by changing directly the RF shield with phosphor bronze mesh material. RESULTS: SPL and vibration measurements demonstrated that eddy-currents induced in the RF shield were the primary cause of acoustic noise. Replacing the conventional solid copper shield with phosphor bronze mesh material altered the vibrations of the RF shield and decreased SPL by 6 to 8 dB at the highest frequencies in EPI, depending on the gradient axis, while boosting the transmit B1 + field by 15%. Padding led to slightly less sound reduction on the X and Z gradient axes, but with minimal impact for the Y axis. CONCLUSION: This study demonstrates the potential importance of eddy-current induced vibrations in the RF coil in terms of acoustic noise and opens new horizons for mitigation measures.

Segmented RF shield design to minimize eddy currents for low-field Halbach MRI systems.

MRI systems have a thin conducting layer placed between the gradient and RF coils, this acts as a shield at the RF-frequency, minimizing noise coupled into the experiment, and decreasing the coupling between the RF and gradient coils. Ideally, this layer should be transparent to the gradient fields to reduce eddy currents. In this work the design of such a shield, specifically for low-field point-of-care Halbach based MRI devices, is discussed. A segmented double layer shield is designed and constructed based on eddy current simulations. Subsequently, the performance of the improved shield is compared to a reference shield by measuring the eddy current decay times as well as using noise measurements. A maximum reduction factor of 2.9 in the eddy current decay time is observed. The segmented shield couples in an equivalent amount of noise when compared to the unsegmented reference shield. Turbo spin echo images of a phantom and the brain of a healthy volunteer show improvements in terms of blurring using the segmented shield.

Pre-excitation gradients for eddy current nulled convex optimized diffusion encoding (Pre-ENCODE).

PURPOSE: To evaluate the use of pre-excitation gradients for eddy current-nulled convex optimized diffusion encoding (Pre-ENCODE) to mitigate eddy current-induced image distortions in diffusion-weighted MRI (DWI). METHODS: DWI sequences using monopolar (MONO), ENCODE, and Pre-ENCODE were evaluated in terms of the minimum achievable echo time (TE min $$ {}_{\mathrm{min}} $$ ) and eddy current-induced image distortions using simulations, phantom experiments, and in vivo DWI in volunteers ( N = 6 $$ N=6 $$ ). RESULTS: Pre-ENCODE provided a shorter TE min $$ {}_{\mathrm{min}} $$ than MONO (71.0 ± $$ \pm $$ 17.7ms vs. 77.6 ± $$ \pm $$ 22.9ms) and ENCODE (71.0 ± $$ \pm $$ 17.7ms vs. 86.2 ± $$ \pm $$ 14.2ms) in 100 % $$ \% $$ of the simulated cases for a commercial 3T MRI system with b-values ranging from 500 to 3000 s/mm 2 $$ {}^2 $$ and in-plane spatial resolutions ranging from 1.0 to 3.0mm 2 $$ {}^2 $$ . Image distortion was estimated by intravoxel signal variance between diffusion encoding directions near the phantom edges and was significantly lower with Pre-ENCODE than with MONO (10.1 % $$ \% $$ vs. 22.7 % $$ \% $$ , p = 6 - 5 $$ p={6}^{-5} $$ ) and comparable to ENCODE (10.1 % $$ \% $$ vs. 10.4 % $$ \% $$ , p = 0 . 12 $$ p=0.12 $$ ). In vivo measurements of apparent diffusion coefficients were similar in global brain pixels (0.37 [0.28,1.45] × 1 0 - 3 $$ \times 1{0}^{-3} $$ mm 2 $$ {}^2 $$ /s vs. 0.38 [0.28,1.45] × 1 0 - 3 $$ \times 1{0}^{-3} $$ mm 2 $$ {}^2 $$ /s, p = 0 . 25 $$ p=0.25 $$ ) and increased in edge brain pixels (0.80 [0.17,1.49] × 1 0 - 3 $$ \times 1{0}^{-3} $$ mm 2 $$ {}^2 $$ /s vs. 0.70 [0.18,1.48] × 1 0 - 3 $$ \times 1{0}^{-3} $$ mm 2 $$ {}^2 $$ /s, p = 0 . 02 $$ p=0.02 $$ ) for MONO compared to Pre-ENCODE. CONCLUSION: Pre-ENCODE mitigated eddy current-induced image distortions for diffusion imaging with a shorter TE min $$ {}_{\mathrm{min}} $$ than MONO and ENCODE.

Broadband Eddy Current Measurement of the Sheet Resistance of GaN Semiconductors.

Although the classical four-point probe method usually provides adequate results, it is in many cases inappropriate for the measurement of thin sheet resistance, especially in the case of a buried conductive layer or if the surface contacts are oxidized/degraded. The surface concentration of dislocation defects in GaN samples is known to challenge this kind of measurement. For the GaN sample presented in this study, it even totally impaired the ability of this method to even provide results without a prior deposition of gold metallic contact pads. In this paper, we demonstrate the benefits of using a new broadband multifrequency noncontact eddy current method to accurately measure the sheet resistance of a complicated-to-measure epitaxy-grown GaN-doped sample. The benefits of the eddy current method compared to the traditional four-point method are demonstrated. The multilayer-doped GaN sample is perfectly evaluated, which will allow further development applications in this field. The point spread function of the probe used for this noncontact method was also evaluated using a 3D finite element model using CST-Studio Suite simulation software 2020 and experimental measurements.

Minimization of eddy current artifacts in sequences with periodic dynamics.

PURPOSE: To minimize eddy current artifacts in periodic pulse sequences with balanced gradient moments as, for example, used for quantitative MRI. THEORY AND METHODS: Eddy current artifacts in balanced sequences result from large jumps in k-space. In quantitative MRI, one often samples some spin dynamics repeatedly while acquiring different parts of k-space. We swap individual k-space lines between different repetitions in order to minimize jumps in temporal succession without changing the overall trajectory. This reordering can be formulated as a traveling salesman problem and we tackle the discrete optimization with a simulated annealing algorithm. RESULTS: Compared to the default ordering, we observe a substantial reduction of artifacts in the reconstructed images and the derived quantitative parameter maps. Comparing two variants of our algorithm, one that resembles the pairing approach originally proposed by Bieri et al., and one that minimizes all k-space jumps equally, we observe slightly lower artifact levels in the latter. CONCLUSION: The proposed reordering scheme effectively reduces eddy current artifacts in sequences with balanced gradient moments. In contrast to previous approaches, we capitalize on the periodicity of the sampled signal dynamics, enabling both efficient k-space sampling and minimizing artifacts caused by eddy currents.

Eddy current-induced artifact correction in high b-value ex vivo human brain diffusion MRI with dynamic field monitoring.

PURPOSE: To investigate whether spatiotemporal magnetic field monitoring can correct pronounced eddy current-induced artifacts incurred by strong diffusion-sensitizing gradients up to 300 mT/m used in high b-value diffusion-weighted (DW) EPI. METHODS: A dynamic field camera equipped with 16 1 H NMR field probes was first used to characterize field perturbations caused by residual eddy currents from diffusion gradients waveforms in a 3D multi-shot EPI sequence on a 3T Connectom scanner for different gradient strengths (up to 300 mT/m), diffusion directions, and shots. The efficacy of dynamic field monitoring-based image reconstruction was demonstrated on high-gradient strength, submillimeter resolution whole-brain ex vivo diffusion MRI. A 3D multi-shot image reconstruction framework was developed that incorporated the nonlinear phase evolution measured with the dynamic field camera. RESULTS: Phase perturbations in the readout induced by residual eddy currents from strong diffusion gradients are highly nonlinear in space and time, vary among diffusion directions, and interfere significantly with the image encoding gradients, changing the k-space trajectory. During the readout, phase modulations between odd and even EPI echoes become non-static and diffusion encoding direction-dependent. Superior reduction of ghosting and geometric distortion was achieved with dynamic field monitoring compared to ghosting reduction approaches such as navigator- and structured low-rank-based methods or MUSE followed by image-based distortion correction with the FSL tool "eddy." CONCLUSION: Strong eddy current artifacts characteristic of high-gradient strength DW-EPI can be well corrected with dynamic field monitoring-based image reconstruction.

Practical considerations of diffusion-weighted MRS with ultra-strong diffusion gradients.

Introduction: Diffusion-weighted magnetic resonance spectroscopy (DW-MRS) offers improved cellular specificity to microstructure-compared to water-based methods alone-but spatial resolution and SNR is severely reduced and slow-diffusing metabolites necessitate higher b-values to accurately characterize their diffusion properties. Ultra-strong gradients allow access to higher b-values per-unit time, higher SNR for a given b-value, and shorter diffusion times, but introduce additional challenges such as eddy-current artefacts, gradient non-uniformity, and mechanical vibrations. Methods: In this work, we present initial DW-MRS data acquired on a 3T Siemens Connectom scanner equipped with ultra-strong (300 mT/m) gradients. We explore the practical issues associated with this manner of acquisition, the steps that may be taken to mitigate their impact on the data, and the potential benefits of ultra-strong gradients for DW-MRS. An in-house DW-PRESS sequence and data processing pipeline were developed to mitigate the impact of these confounds. The interaction of TE, b-value, and maximum gradient amplitude was investigated using simulations and pilot data, whereby maximum gradient amplitude was restricted. Furthermore, two DW-MRS voxels in grey and white matter were acquired using ultra-strong gradients and high b-values. Results: Simulations suggest T2-based SNR gains that are experimentally confirmed. Ultra-strong gradient acquisitions exhibit similar artefact profiles to those of lower gradient amplitude, suggesting adequate performance of artefact mitigation strategies. Gradient field non-uniformity influenced ADC estimates by up to 4% when left uncorrected. ADC and Kurtosis estimates for tNAA, tCho, and tCr align with previously published literature. Discussion: In conclusion, we successfully implemented acquisition and data processing strategies for ultra-strong gradient DW-MRS and results indicate that confounding effects of the strong gradient system can be ameliorated, while achieving shorter diffusion times and improved metabolite SNR.

Rapid Identification of Material Defects Based on Pulsed Multifrequency Eddy Current Testing and the k-Nearest Neighbor Method.

The article discusses the utilization of Pulsed Multifrequency Excitation and Spectrogram Eddy Current Testing (PMFES-ECT) in conjunction with the supervised learning method for the purpose of estimating defect parameters in conductive materials. To obtain estimates for these parameters, a three-dimensional finite element method model was developed for the sensor and specimen containing defects. The outcomes obtained from the simulation were employed as training data for the k-Nearest Neighbors (k-NN) algorithm. Subsequently, the k-NN algorithm was employed to determine the defect parameters by leveraging the available measurement outcomes. The evaluation of classification accuracy for different combinations of predictors derived from measured data is also presented in this study.

A correction algorithm for improved magnetic field monitoring with distal field probes.

PURPOSE: A significant source of artifacts in MRI are field fluctuations. Field monitoring is a new technology that allows measurement of field dynamics during a scan via "field probes," which can be used to improve image reconstruction. Ideally, probes are located within the volume where gradients produce nominally linear field patterns. However, in some situations probes must be located far from isocenter where rapid field variation can arise, leading to erroneous field-monitoring characterizations and images. This work aimed to develop an algorithm that improves the robustness of field dynamics in these situations. METHODS: The algorithm is split into three components. Component 1 calculates field dynamics one spatial order at a time, whereas the second implements a weighted least squares solution based on probe distance. Component 3 then calculates phase residuals and removes the residual phase for distant probes before recalculation. Two volunteers and a phantom were scanned on a 7T MRI using diffusion-weighted sequences, and field monitoring was performed. Image reconstructions were informed with field dynamics calculated conventionally, and with the correction algorithm, after which in vivo images were compared qualitatively and phantom image error was quantitatively assessed. RESULTS: The algorithm was able to correct corrupted field dynamics, resulting in image-quality improvements. Significant artifact reduction was observed when correcting higher-order fits. Stepwise fitting provided the most correction benefit, which was marginally improved when adding the other correction strategies. CONCLUSION: The proposed algorithm can mitigate effects of phase errors in field monitoring, providing improved characterization of field dynamics.

Eddy currents analysis methods for an MRI longitudinal gradient coil.

PURPOSE: The rapid switching of the gradient fields induces eddy currents in neighboring metallic structures, causing undesirable effects. Numerical computations are thus required to understand eddy-currents effects for designing/implementing mitigation (involving passive shielding) and compensating techniques (using pre-emphasis). Previously, the network-analysis (NA) method was introduced to compute z-gradient eddy currents, although limited to a circularly symmetric and unconnected coil. Multi-layer integral method (MIM) method was recently introduced, modifying the circuit equation involving stream functions. We tailor MIM (TMIM) for a more general eddy-currents analysis in thin structures. Z-gradient eddy currents are analyzed and then compared using three methods (NA, TMIM, and Ansys). The analysis helps to evaluate the efficiency of passive shielding and to compensate eddy currents. METHODS: NA and TMIM computational frameworks for harmonic and transient eddy-currents analysis were implemented and cross-validated against Ansys Maxwell. A pre-emphasis pulse was modeled for compensating eddy currents. RESULTS: Eddy-currents analysis of an unconnected z-gradient coil in both the passive shield and cryostat were computed, and results were comparable to the least computationally efficient Ansys simulations. Although NA computations are fast, TMIM is implemented with reasonable efficiency and applied to circularly unsymmetric geometries. TMIM computations were further validated against Ansys using a connected z-gradient. Our computations allowed the effective evaluation of the performance of three various passive-shielding configurations, non-capped, capped, and slitted (for the first time), and an effective pre-emphasis compensation model was computed. CONCLUSION: Three eddy-currents analysis methods were studied and compared. Computationally efficient TMIM allows both harmonic and transient eddy-currents analysis involving different/complex gradient configurations/situations as well as involved shielding structures. Eddy-currents pre-emphasis compensation was demonstrated.

Transient eddy current analysis for a spiral gradient pulse.

Eddy currents are induced in the metallic structures of MRI machines due to the rapid switching of gradient fields generated by gradient coils. Several undesirable effects are associated with the induced eddy currents such as heat, acoustic noise, and MR image distortions. Accurate transient eddy currents numerical computations are required to predict and ameliorate such effects. Spiral gradient waveforms are of importance, particularly for fast MRI acquisition applications. For mathematical convenience, previously published work is mostly concerned with transient eddy currents computations associated with trapezoidal gradient waveforms; where spiral gradient waveforms were not considered. We recently presented preliminary transient eddy currents computations induced by an amplitude-modulated sinusoidal pulse in the scanner's cryostat. In this work, we present a full computational framework for transient eddy currents induced by a spiral gradient waveform. A mathematical model for transient eddy currents involving the spiral pulse was derived and presented in detail using the circuit equation. Computations were implemented using a tailored multilayer integral method (TMIM) and results were compared to Ansys eddy currents analysis for cross-validation. The transient response of resultant fields generated by both an unshielded transverse coil driven by a spiral waveform was computed showing high agreement between Ansys and TMIM; albeit with high computational efficiency concerning time and memory. For further validation, computations for a shielded transverse coil were performed showing how eddy currents effects are reduced.

Non-Destructive Inspection of High Temperature Piping Combining Ultrasound and Eddy Current Testing.

This paper presents an automated Non-Destructive Testing (NDT) system for the in-service inspection of orbital welds on tubular components operating at temperatures as high as 200 °C. The combination of two different NDT methods and respective inspection systems is here proposed to cover the detection of all potential defective weld conditions. The proposed NDT system combines ultrasounds and Eddy current techniques with dedicated approaches for dealing with high temperature conditions. Phased array ultrasound was employed, searching for volumetric defects within the weld bead volume while Eddy currents were used to look for surface and sub-surface cracks. The results from the phased array ultrasound results showed the effectiveness of the cooling mechanisms and that temperature effects on sound attenuation can be easily compensated for up to 200 °C. The Eddy current results showed almost no influence when temperatures were raised up to 300 °C.

Practical Aspects of Instantaneous Magnetization Power Functions of Silicon Iron Laminations.

Magnetic energy loss P of SiFe steel represents a key factor for the efficiency of soft magnetic machine cores. Traditionally, they are operated with 50 Hz (or 60 Hz), a frequency value that yields rather balanced portions of hysteresis loss and eddy current loss. In equivalent circuits of transformers, P tends to be represented by a magnetic power resistance R M, as a constant. For the most important case of sinusoidal induction B of 50 Hz, this would correspond to an instantaneous magnetization power function p(t) that is sinusoidal as well, however, with 100 Hz (or 120 Hz). On the other hand, from complex, non-linear mechanisms of hysteresis, it is obvious that p(t) should be strongly non-sinusoidal, even for exactly sinusoidal B(t). So far, almost all corresponding instantaneous investigations were restricted to calculated modelling of loss portions and transient modelling. On the other hand, for the first time, the present study was focussed on functions p(t) as measured at IEC-standardized samples of industrially relevant steel. Practical evaluations are discussed with respect to the revealed "history" of magnetization processes, as well as for product characterization. For these tasks, a novel digitized "Low-mass Single Sheet Tester" was developed that was applied for both non-oriented steel (NO) and grain-oriented steel (GO), for 50 Hz. Interpretations proved to be favoured by relating p(t) to total P, according to an instantaneous power ratio. As a result, both steel types revealed strongly non-sinusoidal power functions, with short durations of negative p. Negative p proved to be most pronounced for NO steel, as a measure for the onset of reversible turns of atomic moments. As a consequence, p(t) comprises strong upper harmonics of 200 Hz and even 300 Hz. Based on theoretical considerations, we split p(t) in a dissipative loss power function p L(t) and in a potential energy power function p P(t). Finally, we used p(t) to determine the corresponding power resistance R M(t) that proves to be a distinctly nonlinear function as well. It resembles a rectified co-sinus, also exhibiting short negative spikes that reflect the crystallographic dis-orientation of the polycrystalline material.

Fluxgate Sensor with Bifactor Excitation Mode.

The paper considers non-destructive testing (NTDs) as a means to solve the flaw detection problems of magnetic products. It proposes a new probe-coil magnetic-field NDT, not requiring the pre-magnetization of the test object material, which is mandatory for all conventional magnetic flaw detection techniques. A new bifactor excitation of the fluxgate sensor's sensitive element, based on double µ-transformation through the simultaneous activation of magnetic-modulating and electromagnetic-acoustic effects, is theoretically justified. The physical processes underlying the proposed technique are considered in detail, and a scheme for its practical implementation is described. The authors provide a variant of the new fluxgate's original design, implementing the proposed excitation technique. The specifics of implementing the fluxgate operating modes are analyzed, testifying to the possibility of detecting a given class of flaws with the required coverage as well as ensuring the required diagnostic resolution during flaw detection, which, in fact, indicates a more reliable identification of both the flaw type and location. Herewith, the new fluxgate type features the advantages of improved functionality and lower cost due to its simple design. The paper also considers a method to experimentally study the capabilities of the proposed fluxgate sensor with a new bifactor excitation in detail. The results of the experimental study into its key specifications are provided, confirming its high resolution, narrower zone of uncertainty, and the possibility of detecting smaller flaws at greater depths compared to available analogs.

Model-based determination of the synchronization delay between MRI and trajectory data.

PURPOSE: Real-time monitoring of dynamic magnetic fields has recently become a commercially available option for measuring MRI k-space trajectories and magnetic fields induced by eddy currents in real time. However, for accurate image reconstructions, sub-microsecond synchronization between the MRI data and field dynamics (ie, k-space trajectory plus other spatially varying fields) is required. In this work, we introduce a new model-based algorithm to automatically perform this synchronization using only the MRI data and field dynamics. METHODS: The algorithm works by enforcing consistency among the MRI data, field dynamics, and receiver sensitivity profiles by iteratively alternating between convex optimizations for (a) the image and (b) the synchronization delay. A healthy human subject was scanned at 7 T using a transmit-receive coil with integrated field probes using both single-shot spiral and EPI, and reconstructions with various synchronization delays were compared with the result of the proposed algorithm. The accuracy of the algorithm was also investigated using simulations, in which the acquisition delays for simulated acquisitions were determined using the proposed algorithm and compared with the known ground truth. RESULTS: In the in vivo scans, the proposed algorithm minimized artifacts related to synchronization delay for both spiral and EPI acquisitions, and the computation time required was less than 30 s. The simulations demonstrated accuracy to within tens of nanoseconds. CONCLUSIONS: The proposed algorithm can automatically determine synchronization delays between MRI data and field dynamics measured using a field probe system.

Heating of metallic biliary stents during magnetic hyperthermia of patients with pancreatic ductal adenocarcinoma: an in silico study.

OBJECTIVE: To investigate the eddy current heating that occurs in metallic biliary stents during magnetic hyperthermia treatments and to assess whether these implants should continue to be an exclusion criterion for potential patients. METHODS: Computer simulations were run on stent heating during the hyperthermia treatment of local pancreatic tumors (5-15 mT fields at 300 kHz for 30 min), considering factors such as wire diameter, type of stent alloy, and field orientation. Maxwell's equations were solved numerically in a bile duct model, including the secondary field produced by the stents. The heat exchange problem was solved through a modified version of the Pennes' bioheat equation assuming a temperature dependency of blood perfusion and metabolic heat. RESULTS: The choice of alloy has a large impact on the stent heating, preferring those having a lower electrical conductivity. Only for low field intensities (5 mT) and for some of the bile duct tissue layers the produced heating can be considered safe. The orientation of the applied field with respect to the stent wires can give rise to the onset of regions with different heating levels depending on the shape that the stent has finally adopted according to the body's posture. Bile helps to partially dissipate the heat that is generated in the lumen of the bile duct, but not at a sufficient rate. CONCLUSION: The safety of patients with pancreatic cancer wearing metallic biliary stents during magnetic hyperthermia treatments cannot be fully assured under the most common treatment parameters.

Calculated versus measured iron losses and instantaneous magnetization power functions of electrical steel.

Magnetic energy loss P of soft magnetic laminations like SiFe sheets tends to be expressed through an integral over the power product H · dB/dt. Already in earlier papers, we stressed that distinctions are needed for the quantities H and B. However, they are not considered in practically consistent ways, in the so far literature. Here, we discuss these distinctions in closer ways, comparing loss determination by calculation and measurement, respectively. A physically consistent procedure is described for the determination of loss and magnetization power functions through measurement of bi-located quantities H S and B C (S surface, C cross section). On the other hand, it is concluded that corresponding quantitative calculations-based on co-located quantities H and B-are impeded by the high amount of technological parameters of modern steel products. For example, they result from chemical additions, and-in particular-also from specific technologies of rolling, annealing, coating or scribing.

Fully automated background phase correction using M-estimate SAmple consensus (MSAC)-Application to 2D and 4D flow.

PURPOSE: Flow quantification by phase-contrast MRI is hampered by spatially varying background phase offsets. Correction performance by polynomial regression on stationary tissue may be affected by outliers such as wrap-around or constant flow. Therefore, we propose an alternative, M-estimate SAmple Consensus (MSAC) to reject outliers, and improve and fully automate background phase correction. METHODS: The MSAC technique fits polynomials to randomly drawn small samples from the image. Over several trials, it aims to find the best consensus set of valid pixels by rejecting outliers to the fit and minimizing the residuals of the remaining pixels. The robustness of MSAC to its few parameters was investigated and verified using third-order polynomial correction fits on a total of 118 2D flow (97 with wrap-around) and 18 4D flow data sets (14 with wrap-around), acquired at 1.5 T and 3 T. Background phase was compared with standard stationary correction and phantom correction. Pulmonary/systemic flow ratios in 2D flow were derived, and exemplary 4D flow analysis was performed. RESULTS: The MSAC technique is robust over a range of parameter choices, and a unique set of parameters is suitable for both 2D and 4D flow. In 2D flow, phase errors were significantly reduced by MSAC compared with stationary correction (p = 0.005), and stationary correction shows larger errors in pulmonary/systemic flow ratios compared with MSAC. In 4D flow, MSAC shows similar performance as stationary correction. CONCLUSIONS: The MSAC method provides fully automated background phase correction to 2D and 4D flow data and shows improved robustness over stationary correction, especially with outliers present.