Gradient impulse response functions have recently been introduced to characterize MR gradient systems with high accuracy (1). This information can be employed to estimate gradient trajectories for enhanced image reconstruction (2,3) and RF-pulse design (4), or to tune the gradient system’s pre-emphasis settings. The underlying assumption is that the system is linear and time-invariant. However, thermal drifts of the system can cause a violation of the latter assumption (5–7), thereby limiting the accuracy/applicability of the method.

To overcome this problem, we present a novel method where the gradient response is continuously characterized. Here, field measurements are repeatedly performed during the MR sequence. From multiple field measurements (harvest) and the known MR sequence gradients, the gradient response is calculated. Frequency components that are not present in the MR sequence input are not characterized. Conversely, these components are not required when utilizing the gradient response for the same sequence. The benefit of the method is demonstrated by obtaining the continuous gradient output of MR sequences and first imaging results are presented.

All experiments were conducted on a 3T-MR system (Philips Healthcare, Netherlands). Eight ¹⁹F-based field probes (8) (T2=~2ms) were mounted to a head receive coil array (Fig.1left). For probe excitation and probe/coil data acquisition a dedicated RF-pulse generator and spectrometer were used. The position of the probes were obtained in an initial calibration step (9). Thereafter, a 2D-SSh-EPI (resolution=(1.3mm)², TE=61ms, TR=150ms, 20 slices) with 128 dynamics (duration=6:27min) was performed. During the MR sequence, the probes were repeatedly excited (TR_probe=6.005ms) followed by a readout of 500µs (Fig.1right). From the probes data the gradient output during each readout was calculated (9), filtered to a bandwidth of ±50kHz and gridded to the same time resolution (6.4µs) as the gradient input. The gradient response was subsequently determined by solving the linear system

$$o=Ic$$

Here $$$o$$$ denotes a vector (Nx1) of multiple output gradient readouts. $$$I$$$ denotes a matrix (NxM) with each row holding a timeframe of the input waveform $$$i_{cont}$$$, each row being shifted by the time relating to the corresponding sample in $$$o$$$. The vector $$$c$$$ (Mx1) denotes the unknown gradient response (Fig.2). For each gradient response calculation, 1300 output readouts were used (N=~50000, total harvesting time of 7.8s). The length of the gradient response function was chosen to be 40ms (M=6025).

Finally, the continuous gradient output $$$o_{cont}$$$ was calculated by multiplying a continuous input matrix $$$I_{cont}$$$ with the obtained response:

$$o_{cont}=I_{cont}c$$

For demonstration, the gradient responses were evaluated for the first $$$c^{(first)}$$$ and last $$$c^{(last)}$$$ portion of the EPI sequence for the read gradient axis.

The method was repeated for a gradient echo sequence (TR=50ms, TE=5ms, resolution=(1.4mm)²). Gridding based image reconstruction was performed using the obtained k-space trajectory.

The obtained continuous gradient output $$$o_{cont}$$$ matched the measured gradients $$$o$$$ up to the noise level (Fig.3), indicating the validity of the linearity and time-invariance assumption during the total acquisition time of $$$o$$$. $$$o_{cont}$$$ showed effects from eddy currents and fine mechanical vibrations, demonstrating the sensitivity of the method. The response functions calculated from the beginning $$$c^{(first)}$$$ and the end $$$c^{(last)}$$$ of the EPI sequence, showed shifts of oscillatory terms as well as a global broadening in the frequency domain (Fig.4left), which were also reflected in the gradient time courses $$$o_{cont}^{(first)}$$$ and $$$o_{cont}^{(last)}$$$ (Fig.4right). The obtained k-space data for the gradient echo scan allowed for a faithful image reconstruction (Fig.5).

We introduced the concept of gradient response harvesting. Unlike gradient response measurements using a dedicated calibration sequence, the approach assumes/tolerates slow variations of the gradient response.

An important application is the possibility to obtain continuous field data, which was also demonstrated in this work, including first image reconstruction results. Here, the approach benefits from allowing gaps between probe data readouts. This drastically reduces probe hardware requirements, which have so far prohibited alternative continuous monitoring approaches (10) to be performed simultaneously with the MR experiment.

The method can be straightforwardly extended to also account for gradient cross-terms. Other means of calculating the gradient response, e.g. that include additional priors such exponential decay of eddy currents, may as well be employed. Moreover, the temporal variability/update and required frequency resolution of the gradient responses are to be further investigated. Here, a combination with field feedback control (11) to address slow non-linear field deviations may be attractive.

Apart from obtaining continuous gradient/trajectory information, the method may also be tested for real-time pre-emphasis tuning or continuous system diagnostics. The accuracy and general applicability of this method offers the possibility to increase system performance and enhance a wide range of MR applications.