During EPI, apparent translation along the phase encoding direction resulted from a drift in resonance frequency (). Image displacement increases during EPI acquisition, and decreases subsequently, both in an exponential manner. The process is slow suggesting a thermal origin. Image sets obtained with two different EPI-readout frequencies were compared: one in resonance with the principal mode of vibration of the gradient coil system, the second off-resonance. The large difference in frequency drift, and the consequent apparent object dislocation can only be explained by a thermal process that involves mechanical vibration, since the two protocols were otherwise almost identical (see ). The small alteration of the gradient amplitude and duty cycle does not engender a sufficient difference in power deposition to account for the observed heating effect. The slight variation in the gradient timing is equally unlikely to produce any significant difference in eddy currents that could explain the observed phenomenon. The actively shielded design of the gradient coil set used in this study also supports the argument that eddy currents do not contribute substantially to the observed phenomenon. Therefore, we suggest a process in which friction, between the ferromagnetic shim elements and the shimming slot insert, transforms the vibration energy into heat, increasing the temperature and reducing the magnetization of the shim elements, thereby changing the scanner's magnetic field.
The analysis of the linewidth () indicates the presence of dynamic line broadening effects during the EPI acquisition, which might be due to residual eddy currents, but more likely are the result of the vibration of the assembly itself producing an acoustic-magnetic coupling as reported by Wu et al.(16
). A second thermal mechanism might be responsible for the faster recovery of the linewidth after EPI acquisition, compared to that of the frequency shift; this effect is small in comparison to the large drift of the static magnetic field and does not produce visible image artifacts. This second order effect is probably related to thermal dilatation of the coil assembly, thereby slightly changing the position of the passive shim elements, and consequently introducing small high-order alterations in the magnetic field.
Two different heat-transfer processes can explain the bi-exponential behavior of the frequency shift during recovery: Specifically, we suggest that the two different time constants result from heat conduction between A) the ferromagnetic shim elements and the whole coil assembly (slow heat-exchange pathway), and, B) the coil system and the water-cooling circuit (fast heat-exchange pathway). In this model, the water-cooling system is a thermal reservoir with (approximately) constant temperature; it is also strongly coupled to the coil assembly, which has a far larger heat capacitance than the small shim elements. During EPI acquisition additional processes have to be considered: The suggested friction-induced heating of C) the shim elements, and, D) other vibrating parts of the coil assembly, and finally, E) the Joule transformation of electric energy to heat in the resistive copper wires. illustrates the complete model.
Figure 9 Schematic heat transfer model. Heat exchange pathways A and B between the shim elements, coil assembly, and the water cooling system are responsible for bi-exponential temperature decay during system recovery. Two energy sources contribute during EPI (more ...)
For the mono-exponential field-increase during EPI acquisitions, we found that the time constant, which results from both the “slow” and “fast” thermal pathways, is longer for the “Quiet” protocol, compared to the “Loud” protocol. This suggests that for the lower energy deposition during “Quiet” scans, the “slow” thermal pathway has a relatively higher contribution. During “Loud” scans, the high-energy deposition caused by vibration of the whole coil assembly might overload the water-cooling pathway. For the bi-exponential field-recovery without EPI acquisition, we recorded the same short time constant for “Quiet” and “Loud” protocols, demonstrating the same “fast” pathway with time constant, τ1
40 min. The long time constant (τ2
) was smaller for the “Quiet” compared to the “Loud” protocol; however, its relative amplitude (A2
) was higher for the former. This finding also suggests that the “slow” thermal pathway is slightly dominant when the vibration is less intense (“Quiet” scans). Lastly, the longer mono-exponential recovery of the linewidth (FWHM) during “Quiet” scans also supports the dominance of the “slow” pathway for the “Quiet” scans. To gain more insight about the involved thermal processes it would be desirable to simplify the possible thermal pathways by switching off the water-cooling system; unfortunately, hardware limitations did not allow this in the present study.
The zero-order magnetic field change (frequency drift) introduces large apparent motion artifacts in the time series over a 2 hour EPI acquisition (: 8mm for “Loud”, and 2 mm for “Quiet” scans), in agreement with previous studies(17
). We demonstrated that this artifact can be reduced to a small remaining displacement of less than 0.2 mm, by applying a time-domain linear phase correction based on measurements of the frequency drift. The remaining apparent displacement represents the sensitivity limit of the method due to noise in the frequency offset acquisition, curve fitting errors, and statistical noise in the realignment process used to quantify the displacement.
The in vivo study demonstrates that the observed frequency drift varies slowly enough over time to be linearly approximated. Therefore, the frequency drift can be corrected with only two measurements of the resonant frequency: immediately before and after the acquisition of the time series. The activation maps demonstrate that the frequency drift correction successfully suppresses spurious activation due to apparent motion ().
Slowly varying frequency drifts have been reported repeatedly(17
). The resulting apparent motion artifacts(3
) can be corrected either by directly removing the frequency drift as demonstrated here or by standard image realignment(9
). However, realignment algorithms can eventually introduce spurious activation even in the absence of real object motion(23
). Although this is not generally considered to be a serious problem we would like to alert about the possibility, especially when using low frequency stimulation models. The prior removal of frequency drifts, as described here, can potentially turn the common retrospective for real object motion more robust, thereby avoiding possible spurious activation in fMRI. Compared to corrections derived from phase measurements(19
), our approach has superior sensitivity (< 10−3
ppm/time point) in detecting frequency drifts and other sufficiently slow instabilities.