Dynamic operation of higher-order shim fields is compromised by a number of mechanisms, most prominent of which are eddy currents. To counteract the effects of eddy currents it is common to pass the input waveform through a preemphasis filter, which traditionally consists of a sum of exponentially decaying terms^1,2. The parameters of the exponentials are typically determined through an image-based eddy current characterization process. Recent advances in field measurement technology, however, permit more rapid characterization of shim field dynamics^3,4. This can be utilized to determine exponential preemphasis parameters, but also reveals features in the field response that go beyond the exponential model, such as oscillatory responses. Based on such characterization it has been proposed to implement non-parametric preemphasis filters constructed from the inverse of the shim impulse response function (SIRF)⁵, which has the potential of yielding more comprehensive control over the system’s frequency response.

In this work we investigate the utility of the different preemphasis approaches for higher-order shim updating. Specifically we compare i) traditional image-based eddy current characterization vs. SIRF-based parameter extraction for exponential preemphasis, and ii) exponential preemphasis vs. non-parametric preemphasis based on the SIRF inverse.

Shim system characterization was performed on a Siemens Magnetom 7T system with dynamically operated 2^nd order spherical harmonic shims. The Siemens Healthcare Tx-Array system provided full waveform control of the input to the shim amplifiers (Resonance Research Inc.) with software preemphasis consisting of up to five exponential terms. Like on most present-day systems, the higher-order shim coils were not shielded.

Standard image-based eddy current characterization was obtained by acquiring a field map of a spherical phantom at different delay times after a shim step. Each field map was fitted to a spherical harmonic spatial basis set, and the shim field time decay was fitted to a set of 2-3 exponential terms. Amplitudes and time constants of the exponential preemphasis terms were subsequently calculated as described by Jehenson et al¹. For fine-tuning of the parameters, the process was repeated once with the initially calculated preemphasis applied.

Additionally, the SIRF of each shim channel was measured with a 3^rd-order dynamic field camera (Skope Magnetic Resonance Technologies) using the method described in Ref. (4). Frequency-swept test pulses were input to the shim system while monitoring the resulting output field. A frequency-domain deconvolution of the output by the input then yields an accurate and detailed estimate of the system frequency response (Fig. 1).

Based on the measured SIRF, preemphasis filters were calculated in three ways: 1) by fitting three exponential terms to the ideal compensatory step response in the time domain, 2) by performing a frequency-domain fit of 1/SIRF, using a model of three exponential compensation terms, 3) by calculating a non-parametric preemphasis filter as $$$H_t/SIRF$$$, where $$$H_t$$$ was defined as a target system response of 3 kHz bandwidth⁵ (Fig. 2).

To evaluate preemphasis performance, field camera measurements of shim field responses to stepped shim pulses using the different preemphasis implementations were measured. Additionally, the full SIRF was remeasured using exponential and non-parametric preemphasis.

Both exponential and non-parametric preemphasis eliminated the central peak, corresponding to long-living eddy currents, in the measured SIRFs (Fig. 3). However, while the exponential preemphasis merely raised the response at higher frequencies, the non-parametric filter shaped it to closely follow the target, thereby actively suppressing resonances. In the time-domain, the non-parametric filter yielded 5-10 ms faster settling time after a shim update and was able to suppress field oscillations induced by the step (Fig. 4). Comparing the different versions of exponential preemphasis, all were able to achieve eddy current compensation to within ±1% of the step amplitude after an initial settling period of about 10 ms (Fig. 5). A slight advantage for the SIRF-based frequency-domain fit was observed in some of the shim channels.

Long-living eddy currents induced in cold structures of the cryostat are well described by an exponential model, and can thus be sufficiently compensated with traditional preemphasis. Higher-frequency components of the system response, however, are not well captured by the exponential model. These can be addressed by using a non-parameteric preemphasis filter based on the SIRF inverse.

In practice, exponential preemphasis should suffice for applications where a settling time of 10 ms or greater is acceptable. For faster shim updates, however, a more comprehensive model is needed. Shim operation beyond simple step-wise updating likely also stands to benefit from the improved frequency response of the non-parametric preemphasis filter.