IEEE TRANSACTIONS ON BIOMEDICAL ENGINEERING, VOL. 55, NO. 9, SEPTEMBER 2008 2115 Acoustic fMRI Noise: Linear Time-Invariant System Model Carlos V. Rizzo Sierra ∗ , Student Member, IEEE, Maarten J. Versluis, Johannes M. Hoogduin, and Hendrikus (Diek) Duifhuis, Senior Member, IEEE Abstract—Functional magnetic resonance imaging (fMRI) en- ables sites of brain activation to be localized in human subjects. For auditory system studies, however, the acoustic noise gener- ated by the scanner tends to interfere with the assessments of this activation. Understanding and modeling fMRI acoustic noise is a useful step to its reduction. To study acoustic noise, the MR scanner is modeled as a linear electroacoustical system generating sound pressure signals proportional to the time derivative of the input gradient currents. The transfer function of one MR scanner is determined for two different input specifications: 1) by using the gradient waveform calculated by the scanner software and 2) by using a recording of the gradient current. Up to 4 kHz, the first method is shown as reliable as the second one, and its use is encour- aged when direct measurements of gradient currents are not possi- ble. Additionally, the linear order and average damping properties of the gradient coil system are determined by impulse response analysis. Since fMRI is often based on echo planar imaging (EPI) sequences, a useful validation of the transfer function prediction ability can be obtained by calculating the acoustic output for the EPI sequence. We found a predicted sound pressure level (SPL) for the EPI sequence of 104 dB SPL compared to a measured value of 102 dB SPL. As yet, the predicted EPI pressure waveform shows similarity as well as some differences with the directly measured EPI pressure waveform. Index Terms—Acoustic noise, fMRI, gradient noise, linear system, SPL. I. INTRODUCTION F UNCTIONAL magnetic resonance imaging (fMRI) has successfully become an essential tool in human brain imag- ing since first proposed in 1990 [1], [2]. However, fMRI acous- tic noise is a concern for the medical imaging and engineering community, since it exposes volunteers, patients, operators, and medical practitioners to doses of high-level sound for periods of time in the order of hours. 1 Effects of this airborne sound ex- posure range from potential hearing loss to nonlinear effects on brain activation in patients and volunteers [3]–[7]. Even though for the latter there are timing modifications in image acquisi- Manuscript received June 19, 2007; revised January 31, 2008. Asterisk indi- cates corresponding author. ∗ C. V. Rizzo Sierra is with the Department of Biomedical Engineering, Fac- ulty of Mathematics and Natural Sciences, University of Groningen, NL 9747 AG Groningen, The Netherlands (e-mail: c.rizzo@med.umcg.nl). M. J. Versluis is with MR Clinical Packages, Philips Medical Systems, 5680 DA Best, The Netherlands. J. M. Hoogduin is with the 7T MR Group, University Medical Center Utrecht, 3508 GA Utrecht, The Netherlands (e-mail: j.m.hoogduin-1@umcutrecht.nl). H. (Diek) Duifhuis is with the Department of Physics and Applied Physics, University of Groningen, NL 9747 AG Groningen, The Netherlands. Digital Object Identifier 10.1109/TBME.2008.923112 1 Note that, for regular MRI, less or similar sound levels apply. However, in that case, the exposure duration is greatly reduced. tion, such as sparse sampling, [8]–[10] aimed at reducing the influence of noise on brain activity, they are not generally ap- plied because they compromise data acquisition efficiency. Also, earplugs or other protectors that are worn by subjects [11] are not sufficient to achieve acceptable quiet conditions [12], [13]. The mechanism and process that produces the gradient mag- netic field is the primary source of this noise. That is, the gra- dient coils that use strong currents within the static background magnetic field create Lorentz forces, as detailed in [14]. These currents are necessary to produce the spatially and temporally varying magnetic fields required for imaging. In previous stud- ies [15], [16] of the acoustic scanner noise, it has been proposed that the physical structure of the MR scanner behaves as a linear time-invariant (LTI) electroacoustical system, where gradient coil currents I (t) can be interpreted as input and generated sound pressure signals p(t) as outputs of the LTI-system. Physi- cally, the system is made of the mechanical structure of the MR scanner, including magnet, gradient coils, RF body coil, sup- port structures, and the structure of the acoustic space inside the body coil, where the patient would typically be exposed to the noise. The assumption that the scanner noise follows LTI system properties goes back to 1997 [15]. Experimental application and verification of this assumption, however, remains scarce. In a short letter [16], this approach is explicitly advocated, and in studies [17] and [18], the first attempts of such an analysis have been reported. Following this LTI approach, the ratio of output and input spectra defines the classical electroacoustical transfer function [19] H(f ) of this system. A good number of studies [15], [20]–[24] deal with just acoustic noise measurements during conventional anatomical MRI. Hedeen et al. [15] expanded the analysis and reported that acoustic noise signatures were associated with gradient pulse waveforms. They proposed that a common transfer function consistently relates the acoustic noise responses to the gradient currents. A second group of studies deals with acoustic noise measurements during functional MRI [25]–[29]. Here, we also focus on the sound produced in fMRI studies. Since almost all of these studies use echo planar imaging (EPI) sequences [2], [30] which imply the choice of rapid gradient switching, the gen- eration of high-level acoustic noise [25], [31] is a straight- forward consequence. This study models single-shot gradient- echo EPI [2] acoustic noise using the LTI system theory. Therefore, our model attempts to characterize and predict this noise by: 1) estimation of the MRI electroacoustical transfer functions for each gradient coil using pulses as inputs (both as soft- ware gradient waveform and as recorded gradient current); 0018-9294/$25.00 © 2008 IEEE