A publication by Christian Mirkes, Researcher at Skope MR Technologies

30 Oct 2020

When performing the monitoring experiment concurrently with the MRI scan, the field probes must be combined with the present MR setup consisting of the MR scanner, the MR coil and other equipment within the scanner bore. MR imaging requires the switching of time-varying magnetic field gradients. These field gradients induce eddy currents in the conducting structures of the MR scanner and other equipment within the scanner bore. Depending on the size, shape and electrical properties of these structures, the generated fields can extend over the entire imaging volume or can be very local without having a significant impact on image encoding. Some examples of such local structures are:

  • RF shield of the MR coil
  • Electronic components of the MR coil such as cable traps
  • Other appliances that are attached to the MR coil such as mirrors, visual stimulation equipment

The phase measured by each field probe has global and local field contributions. A priori, it is not possible to tell the two sources apart. Global field effects are detected by the entire field probe array and can be correctly represented by the spatial field expansion (assuming a sufficient number of field probes and an adequately chosen basis for the field expansion). Local field effects can corrupt the spatial field expansion and lead to artefacts during image reconstruction.

The negative impact of local eddy currents on image reconstruction can be reduced by carefully choosing the location of the field probes and their surroundings. However, geometric constraints dictated by an already existing MR coil and requirements for the spatial distribution of the field probes might limit the optimization space. Often, some contributions from local fields will be inevitable.

In this document, we demonstrate a method to calibrate NMR field probes and remove fields from eddy currents induced by local hardware components.



A mathematical local eddy current model is created based on one or more calibration scans and is adjusted for each scan session. The model is used to predict the generated local eddy currents for a given imaging sequence. The probe phase accrual caused by the local eddy current fields is subtracted from the measured phase and the corrected probe phase values are used for the spatial field expansion. The obtained k-space trajectories can be used to reconstruct images that are free of artefacts caused by local eddy current contributions.

Generation of the probe-based local eddy current model

As depicted in Figure 1, the acquisition of the data to create a probe-based local eddy current model is performed in two stages. In stage 1, the field probes are positioned within the imaging volume of the MR coil. A holder is used to guarantee an optimal arrangement of the probes. The field probes should cover the imaging volume and allow for a spatial expansion of the field. During an MRI experiment these field probes experience identical eddy current fields as the imaging object positioned at the same location would; essentially the spatio-temporal field dynamics without the influence of the local eddy currents carried by the MR coil. In step 1, one or more sequences with gradient activity on each physical axis are played out. Each field probe measures at its spatial location the phase evolution (φmeas) created by the magnetic field gradients that the scanner plays out (step 2). The field probe phase data is used to perform a linear or higher-order spatial field expansion and calculate the reference k-space trajectories that are free of contributions from local eddy currents (step 3). The reference k-space trajectories are stored on disk to be used for the generation of per-probe eddy current model deployable in a concurrent MRI scan session on the same day or later. In stage 2, the field probes are mounted to their assigned positions on the MR coil or another holding structure used in the concurrent MRI/field-monitoring experiment. The same sequences as used in stage 1 are played out again by the scanner (step 4). The field probes measure the field evolution created by the applied gradient fields, this time also capturing potentially induced local eddy current fields (step 5). Similar as before (step 3), a linear or higher-order spatial field expansion is performed on the potentially corrupted phases to calculate k-space trajectories (step 6). The first-order k-space terms are low-pass filtered and used to calculate the corresponding linear gradients via differentiation (step 7). Steps 6 and 7 can be omitted if nominal gradient waveforms are available for the used MR sequence.  Based on the reference k-space trajectories acquired in stage 1, the phase evolution (φexp) expected to be measured by the probes mounted on the coil or another holding structure is calculated (step 8).

Next, a model is determined relating the potentially corrupted probe phases (from step 4) and gradient waveforms (from step 7) to the expected probe phase (from step 8). A simple analytical model [Jehenson et al. (1990), JMR, pp. 264-287] is used to describe the induced local eddy currents for each field probe:

Multi-band spiral trajectory.

where G is the calculated linear gradient waveform for a given physical axis (X, Y, or Z) that is potentially degraded by local eddy current fields, t the time, g(t) the induced eddy-currents, ⨂ represents the convolution operator and e(t) is the impulse-response function that is given by a sum of n decaying exponentials with amplitude an and decay constants τn:

Multi-band spiral trajectory.

where H(t) is the Heaviside step function:

Multi-band spiral trajectory.
Probe-based local eddy current model generation based on two calibration scans.

Application of the probe-based local eddy current model

Figure 2 shows how the created local eddy current model is applied to measured and potentially corrupted probe phase data. Once a local eddy-current model has been established for each field probe of the arrangement in stage 2, the same or a different sequence of magnetic field gradients as used for the calibration can be played out by the scanner (step 10). The field probes measure the field evolution subject to the magnetic field gradients and potentially induced eddy current fields (step 11). A spatial field expansion is performed based on the measured phases (step 12) and the corresponding gradient is calculated (step 13). If a nominal gradient waveform is available for the used sequence, the former can be used instead of the waveform calculated in step 13. The local eddy current model is used to calculate corrected probe phase data based on the measured probe phases and the calculated gradient (step 14). A spatial expansion is performed on the corrected probe phases (step 15). The corrected k-space trajectories (step 16) are stored to disk and can be used for image reconstruction.

Multi-band spiral trajectory.
Field-monitoring subject to local eddy currents and correction thereof.


The presented method allows to remove local eddy current components from the measured field probe phases. This additional calibration step allows for a more flexible positioning of the field probes in an existing MR setup.