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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