Peter Mazurkewitz^{1}, Jürgen Rahmer^{1}, and Peter Börnert^{1}

^{1}Philips Research Europe, Hamburg, Germany

### Synopsis

Gradient-impulse-response-function
(GIRF) measurement is a well-established method for MRI gradient-system characterization.
Typical GIRF input-functions are triangles or chirps. For triangles, measurements
have to be performed with different pulse lengths to get a continuous frequency
spectrum due to blind spots in the spectrum, requiring long scan times. In
contrast, the spectrum of the chirp waveform covers a large frequency range
without blind spots. However, at low frequencies the chirp fails due to a diverging
intensity in its spectrum. We
interleaved both waveforms and obtained a continuous gradient modulation transfer function (GMTF) spectrum down to low
frequencies in short measurement time.

**Purpose:**

Fast imaging
sequences require rapid switching of strong gradient fields during signal
readout. These field variations generate eddy currents that lead to substantial
deviations from the expected k-space trajectory. Measurement of the gradient
impulse response function (GIRF) is a well-established method for characterization
of MRI gradient system under the assumption of linear time-invariant behavior.
It can be used for characterization of field imperfections, as caused by eddy
currents, concomitant fields, and mechanical gradient coil oscillations^{1} and for the derivation of more
accurate k-space trajectories^{2}.
Different input
functions are used for GIRF measurements like triangles^{3} or so-called chirps^{4}. For triangles,
repeated measurements have to be performed with different triangle pulse
lengths to get a continuous frequency spectrum due to blind spots in the
triangle spectrum, which is a squared Sinc function (Fig. 1 bottom, green). This approach thus
requires long scan times of 1 hour and more^{5}. In contrast, the spectrum of the
chirp waveform (Fig. 1 bottom, blue) covers a large frequency range without blind spots and with high
spectral density and therefore enables time-efficient measurement of the GIRF
in a single scan per gradient axis. However, at low frequencies, its spectral
density approaches zero, leading to a diverging intensity in the spectrum of
the gradient modulation transfer function (GMTF), i.e. the Fourier transform of
the GIRF. To overcome the disadvantages of the individual
methods, we interleave both waveforms in a single measurement to obtain a
continuous GMTF spectrum down to low frequencies in short measurement time.

**Methods:**

Measurements were performed on a 3T Philips Ingenia system (Philips
Healthcare, Best, The
Netherlands)
with a spherical phantom (diameter: 17cm, standard CuSO4 solution) without
additional hardware. We used the method of generating a virtual 1D test probe
by thin slice selection^{6} for all three gradient axes. To probe the spatial
variation of the system response, we shifted the positions in selection
direction^{7}, so that we acquired signal from three stacks (x-, y-,
z-gradient) with four slices each (slice distance 20mm, thickness 1.4mm). The duration
of the applied slew-rate limited chirp^{4} is 80ms and its frequency modulation
ranges from 400Hz to 10kHz. The acquisition window is also 80ms, the maximal
gradient strength is 30mT/m, and the maximum slew rate is 200mT/m/ms. The triangle
shaped gradient, needed for the low frequency characterization, has a duration
of 4ms and a maximal gradient strength of 10mT/m. The acquisition window is 80ms
as well (Fig. 1, top). The complete measurement time was approx. 3 minutes. The
GMTFs of the chirp, of the triangle, and the combination of both^{3} were calculated in terms of 0^{th},
1^{st}, and 2^{nd} spatial order along the gradient direction
(Figs. 2 and 3, left: chirp, mid: triangle, right: combination).

**Results:**

The GMTF of
the measurement using only the chirp waveform shows a well tempered behavior
above approx. 100Hz, but is very unreliable below this frequency. In contrast,
the GMTF of the triangle can be used for frequencies below 200Hz. A combination
of both by a spectral weighted superposition gives a smooth spectrum with good
SNR over the frequency range of interest. This can be observed in all spatial
orders evaluated.

**Discussion and Conclusion:**

For
characterization of the gradient response, we demonstrated that a combination of
chirp and triangle shaped test gradients can significantly reduce scan time
without losing information frequencies below the lower cutoff frequency of the
chirp waveform.

### Acknowledgements

No acknowledgement found.### References

[1] Graedel, N. N. et al. Image reconstruction using
the gradient impulse response for trajectory prediction. Proc. Intl. Soc. Mag.
Reson. Med. 21, 552 (2013)

[2] Campbell-Washburn, A. E. et al. Real-Time
Distortion Correction of Spiral and Echo
Planar Images Using the Gradient System Impulse
Response Function. Magnetic Resonance in Medicine
75, 2278–2285 (2016)

[3] Vannesjo, S. J. et al. Gradient system
characterization by impulse response measurements with a
dynamic field camera. Magn. Reson. Med. 69, 583–593
(2013)

[4] Addy, N. O., Wu, H. H. & Nishimura, D. G.
Simple method for MR gradient system characterization and k-space trajectory
estimation. Magn. Reson. Med. 68, 120–129 (2012)

[5] Vannesjo, S. J. DISS. ETH NO. 21558 (2013)

[6] Duyn, J. H., Yang, Y., Frank, J. A. & van der
Veen, J. W. Simple Correction Method for k-Space
Trajectory Deviations in MRI. J. Magn. Reson. 132,
150–153 (1998)

[7] Gurney, J. M. et al. A simple method for measuring
B_{o} eddy currents. Proc. Intl. Soc. Mag. Reson. Med.13 (2005)