Analysis and Prediction of Gradient Response Functions under Thermal Load
Benjamin E. Dietrich1, Jonas Reber1, David O. Brunner1, Bertram J. Wilm1, and Klaas P. Pruessmann1

1Institute for Biomedical Engineering, University and ETH Zurich, Zurich, Switzerland

Synopsis

Temperature dependent changes of gradient impulse response functions are analyzed by measurements with a recently proposed continuous field camera and the resulting data is used in a locally linear model approach to predict impulse response functions based on temperature data.

Introduction

Most MR imaging and spectroscopy methods rely on highly accurate gradient field-time-courses for signal preparation and encoding. In practice the actual field-time courses often deviate from the ideal pulse program due to hardware limitations and imperfections, such as caused by limited bandwidth of gradient amplifiers, eddy currents and mechanical vibrations. A useful tool to characterize the gradient system and to predict the actual waveforms are gradient impulse response functions (GIRF) [1–3]. However, such impulse response functions can vary under thermal conditions, as has been shown by [4], and thereby challenge the LTI (linear time-invariant) system approach. Especially during long scan sessions with high gradient duty cycles [5] a system heat-up is inevitable, which can lead to erroneous trajectory predictions if a GIRF from a cold system state is used. In order to analyze these changes, a recently proposed continuous field monitoring method [6, 7], based on a dedicated monitoring system [8] and rapidly alternated and re-excited sets of NMR field probes [9–12] is employed. This method/system enables quick response function measurements under varying thermal load. The resulting temperature resolved GIRF data is then fed to a locally linear model to predict GIRFs under thermal load.

Methods

In order to measure GIRFs under different temperature conditions, a series of demanding EPI scans with many readouts (mimicking fMRI experiments), was played out on a Philips Achieva 7 Tesla MRI system (Philips Healthcare, Cleveland, USA). In between these EPI heat-up cycles, gradient response functions were measured. Slice orientations were changed between the heat-up cycles to reach different temperature distributions inside the gradient system. Temperatures were measured with 5 temperature sensors distributed inside the gradient coils. Fig. 2 illustrates the measured temperature profiles and GIRF measurement points. To determine the response functions, frequency sweeps (duration = 10 s) covering a frequency range of 30 kHz were played out by the gradient system. The waveforms did not include any vendor pre-emphasis, since a custom shim control unit was used. The amplitude of the gradient waveforms was set to a small value (1-2 mT/m), such that the measurements did not significantly contribute to the heating processes. The corresponding field responses were then measured with a continuous field camera [7] and the impulse response functions were determined by deconvolution in frequency domain [2].

In a first step a subset of the measured GIRF data was used to generate a linear prediction model: $$$G=T B$$$ , with $$$G$$$ being a matrix where each column is filled with one GIRF (frequency domain representation), $$$T$$$ being a matrix with the corresponding temperature sensor data (each column represents a sensor plus one column with ones for a common offset), and $$$B$$$ the wanted basis for the prediction. To test the model, data from the first 4 measurement cycles was used to predict the GIRFs of the 5th cycle. Training data was selected based on the Euclidean distance in the 5 dimensional temperature space spanned by the 5 temperature sensors, such that the 15 closest temperature configurations of to the training cycles were included in the model. A synthetic EPI waveform was further used (convolved with the predicted and measured GIRFs) to observe the effects in the time domain.

Results

A slight resonance shift (7 Hz) and offset can be observed in the frequency domain representation of the GIRFs under different temperatures (Fig. 3.a). The largest observed deviation between the first “cold” GIRF and the other measurements is 2.7% (Fig. 2.b). As can be seen in Fig. 4, the prediction reduces the error significantly. The result of the exemplary convolution with an EPI waveform revealed errors between “cold” and “hot” GIRFs of up to 270 µT/m (Fig. 5).

Discussion/Conclusions

Heating related changes in the response functions of gradient systems were successfully assessed. The observed resonance shifts and offsets suggest that mechanical properties of the system change due to temperature. While the physical processes behind these effects are very complex, it has been shown that the change in the response function can be predicted to a large degree with a linear model, trained on a sufficiently large data set with temperature conditions similar to the prediction condition. So far only the y gradient response was analyzed, leaving room for further investigations with respect to higher order shims, cross-terms, temperature sensor positioning and number of sensors. The results further suggest that it is possible to predict GIRF changes from temperatures and thereby enable compensation of these changes through, for example, automatic, temperature dependent pre-emphasis.

Acknowledgements

The authors thank Stephen Wheeler and Dr. Roger Lüchinger for the support with the experiments and setup construction.

References

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[2] S. J. Vannesjo, B. E. Dietrich, M. Pavan, D. O. Brunner, B. J. Wilm, C. Barmet, and K. P. Pruessmann, “Field camera measurements of gradient and shim impulse responses using frequency sweeps,” Magn. Reson. Med, vol. 72, no. 2, pp. 570–583, 2014.

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Figures

a) 32 channel field camera. b) Schematic representation of the measurement setup. Sweep pulses for GIRF measurements were played out by the custom gradient control unit controlled by the monitoring system. The heat-up sequences were played out by the scanner console.

a) Temperature profiles of the scan session and GIRF measurement points. The colors of the dots correspond to the line colors in the subsequent figures, illustrating the temperatures of the respective measurements. The yellow shading illustrates the heat-up cycles and the corresponding slice orientation.

a) Effect of temperature on Y channel GIRF. The green curve corresponds to the very first measurement and the blue to the 26th (cf. colors in Fig. 2). The grey shading illustrates the range of the other measurements. b) Standard deviation and maximum deviation with respect to first “cold” measurement.

a) Predicted and measured GIRF corresponding to the last measurement point in the experiment (cf. colors Fig. 2). b) Standard deviation of the prediction error and error without prediction for all measurements of the 5th cycle.

Synthetic EPI waveform according to measured and predicted response behaviour. Significant thermal changes up to hundreds of uT/m are successfully predicted.



Proc. Intl. Soc. Mag. Reson. Med. 24 (2016)
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