In the complex electromagnetic environment of an MRI scanner, any kind of conducting material can experience vibration due to the forces on eddy-currents induced in the conductor by the rapid switching of gradient fields. Such vibration could be dangerous or cause discomfort to the patient.¹ Graf et al. describe a method to measure time-varying torque of a stabilized device, and ISO/TS 10974 gives an overview of good lab practice when conduction measurements of vibration.^2,3 Currently, there does not exist a standardized method to measure device vibration quantitatively. In this project, a method to quantify the gradient-induced vibration of a medical device in an MR system using a Doppler laser vibrometer is presented along with an investigation of its various systematic errors.

All vibration measurements were conducted in a 3T MRI system (Siemens Prisma, Robarts Research Institute, Western University), with a non-contact laser-Doppler vibrometer system (OFV-505/5000, Polytec GmbH, Germany). A copper annulus with an outer diameter of 10 cm, inner diameter of 7 cm, and thickness of 3 mm was suspended with at various positions and orientations in the scanner bore, chosen to maximise the x-component of the magnetic field for the x-gradient. (See Fig 1.). The gradient waveform used was a repeated trapezoidal with rise time of 0.5 ms, flat top time of 100 ms, fall time of 0.5 ms, and off time of 500 ms.

Vibration was recorded with no gradients running, to measure ambient noise of the environment. Furthermore, movement of the apparatus (without the device attached, and with gradients running) was measured to determine vibration caused mechanically or acoustically by the scanner. The displacement of the device was then measured at gradient field strengths of 10, 20, 30 and 40 mT/m, driving only the x-gradient coil. A db/dt probe was placed within several centimeters of the device in order to capture a reference signal indicating the timing and slew rate. This step is critical for the proper analysis of the signals.

Additionally, the device was struck while in the bore to determine its behaviour (without driving gradients). Next, the device was twisted about its vertical axis to observe the effect of the elastics returning the device to equilibrium. Finally, in the lab, the device was struck with a hammer.

A typical measurement is shown in figure 2 along with the corresponding gradient sequence. The device moves on the order of hundreds of microns when the gradient ramps-up and down as the alternating magnetic moment of the device attempts to align itself with the static field. There are two other forms of vibration present as well. One is a low-frequency continuous oscillation between 0 and 50 microns. The other is a fast underdamped harmonic oscillation the device experiences immediately after the gradient coil finishes a ramp. Figure 3 shows a close-up of the device as the gradient field ramps-up to 30 mT/m in 0.5 ms. The annulus was displaced a mean distance of 223 microns and a maximum distance of 363 microns.

Figure 4 shows the comparison of the annulus being struck in the lab to inside the bore, while figure 5 shows how the magnitude of the vibration changes with slew rate.

The vibrations shown in figure 4 are very similar. Both signals resemble that of an underdamped harmonic oscillator. In the bore, the time constant is -553 and has a frequency of 730 Hz. In the lab, the time constant is -25 and has a frequency of 84 Hz. The difference in frequency is explained by an increased elastic restoring force, due to induced eddy currents.

The lower frequency vibration is similar to the vibration within the holding elastic observed in the labs, with no twisting.

The magnitude of vibration increases linearly with slew rate as would be expected. The error was determined from a combination of background noise present in the system, contribution from other sources of vibration, and from the variance of the measurements.

To assess the safety of a device, it is necessary to understand its displacement caused by the gradients ramping, resultant internal vibrations, and the motion of the device with respect to the measurement holder. With the method presented, it should be a straightforward next step to develop a standardized test to measure gradient-induced vibration of any medical device intended for use inside an MRI. A better understanding of this phenomenon will aid in the design of medical devices so as to minimize the vibrations induced.