Specific Issues Related to EEG-fMRI at B ₀ > 3 T

Abstract

Functional MRI (fMRI) can be used to map regional changes in cerebral blood flow and the level of haemoglobin oxygenation (BOLD) associated with neuronal activity (Belliveau et al. 1991; Kwong et al. 1992; Ogawa et al. 1992). In 2003 the US Food and Drug Administration raised the value of the static field of “no significant risk” for MRI to 8 Tesla (T), potentially opening up this technology to large numbers of laboratories in the USA. Regulatory agencies in Europe and Asia reached similar conclusions, and as a result the number of high-field systems worldwide is growing rapidly. The increased static field B ₀ allows the potential for improved signal-to-noise ratio (SNR), offering the possibility of increasing spatial resolution and reducing scan times (Wiesinger et al. 2006; Harel et al. 2006). In this chapter, we outline the safety issues raised and the challenges involved in performing EEG at high-field MRI or at static magnetic fields greater than 3 T.

Appendices

Appendix 1: The Multidimensional Kalman Adaptive Filtering Method

We provide an outline of a 3D extension of the Kalman filter for pulse-related noise cancellation in multiple channels simultaneously based on the adaptive Kalman filter algorithm (Haykin 1996). The adaptive algorithm makes use of any correlation between each of the motion sensor signals m _i (t) and the observed signal y(t c) to estimate the finite impulse response (FIR) kernel (k c) and to remove the noise signals n _i (t, c). Since the true underlying (neuronal) EEG signal s(t,c) is uncorrelated with the motion signals m _i (t), it is unaffected by the adaptive algorithm and, on average, the result of the noise cancellation process ŝ(t, c) will be the true underlying EEG.

Each channel “c” of the EEG signal y(t, c) is modeled as the sum of a “true” underlying EEG signal s(t, c) and a sum of 3D signals n _x (t, c), n _y (t, c) and n _z (t, c) containing motion and ballistocardiogram components along the three cardinal directions:

$y(t,c) = s(t,c) + n_x (t,c) + n_y (t,c) + n_z (t,c)\quad c = 1, \ldots,32.$

((1))

Next, we enumerate the spatial components of both the noise n _i (t,c), i = 1, 2, 3 (i.e. n _x (t,c), n _y (t,c) and n _z (t,c)) and the motion sensor signals m _i (t). The relationship between the noise signals n _i (t,c) and the motion sensor signals m _i (t) is modeled linearly using a time-varying, FIR kernel (k) with the equation:

$n_i (t,c) = \sum\limits_{k = 0}^{N_i - 1} {w_i^t (k,c)m_i (t - k)\quad i = 1,2,3,} $

((2))

where N _i is the order of the FIR kernel (k, c), chosen to be the same for all channels. An adaptive filtering algorithm is used to produce an estimate of the FIR kernel (k, c), which in turn is used to estimate the noise signal n _i (t, c). The sum of estimated noise components signals is then subtracted from the recorded signal y(t, c) to reveal the underlying EEG signal s(t, c),

$\displaylines{ \hat n_i (t,c) = \sum\limits_{k = 0}^{N - 1} {\hat w_i^t (k)m_i (t - k)}, \cr \hat s(t,c) = y(t,c) - \sum\limits_{i = 1}^3 {\hat n_i (t,c)}. \cr} $

((3))

In previous studies (Schomer et al. 2000), we showed that the ballistocardiogram is spatially smooth and that the first eigenvalue of the principal component analysis (PCA) alone accounts for over 90% of the variance. Building on those results, we consider adaptive filtering on the first Q components of the PCA of y(t,c) (i.e. ŷ_q (t): q = 1,…,Q), and select Q according to the desired resulting minimum fractional variance. Figure 6 shows the filtering scheme, which includes: (a) the dimensionality reduction for the 32-channel EEG signals by means of PCA, and (b) singular value decomposition (SVD) transformation along the principal direction of the 3D motion. Figure 6 also illustrates the algorithm with the simplified value of Q = 2, which is a remarkable reduction in computation time: 16 times faster than when Q = 2.

Fig. 6

Adaptive-filtering multichannel scheme used for artifact removal. The input signal (decimated bipolar EEG), after band pass and decimation, is a signal of 32 channels that is first transformed into two principal component analysis (PCA) components. Each component is then separately filtered using the proposed Kalman filter. According to this filtering scheme, three motion sensor signals are first singular value decomposition (SVD) transformed and vectorized before Kalman filtering. After filtering, each “clean” PCA component is used to reconstruct the 32-channel EEG signal. There is a module of Z-10 for causality, given that the motion sensors have an intrinsic delay due to mechanical inertia. Z-L is used to compensate for the Z-10 and the delay in the FIR filter

The synchronization in Fig. 6 occurs because every channel contains a certain mixture of the two filtered PCA components. m ₁(t) is the vector composed of the N samples from the first motion sensor prior to and equal to “t”, m ₂(t) are the data from the second motion sensor, and m ₃(t) are data from the third motion sensor. The matrix m(t) = [m ₁(t) m ₂(t) m ₃(t)] is then separated into three components which are approximately mutually orthogonal, and the final result is obtained by diagonalizing the new motion-sensor covariance matrix ${\bf{\bar m}}(t)$:

$\begin{array}{l} {\rm w(}t + 1,q{\rm ) = }a{\rm w(}t,q{\rm ) + v}_{\rm 3} (t) \\ y_q (t) = {\rm \tilde m}^T (t) \cdot {\rm w}(t,q) + s_q (t) \\ {\rm w}(t,q) = \left[ {{\rm w}_{\rm 1}^t (0,q){\rm w}_{\rm 2}^t (0,q)\quad {\rm w}_{\rm 3}^t (0,q)\quad {\rm w}_{\rm 1}^t (1,q)\quad {\rm w}_{\rm 2}^t (1,q)\quad {\rm w}_{\rm 3}^t (1,q)\quad \ldots \quad {\rm w}_{\rm 1}^t (N,q)\quad {\rm w}_{\rm 2}^t (N,q)\quad {\rm w}_{\rm 3}^t (N,q)} \right]^T \\ {\rm \tilde m(}t{\rm ) = }\left[ {\tilde m_1 (t)\quad \tilde m_2 (t)\quad \tilde m_3 (t)\quad \tilde m_1 (t - 1)\quad \tilde m_2 (t - 1)\quad \tilde m_3 (t - 1)\quad \ldots \quad \tilde m_3 (t - N + 1)} \right]^{\rm T} . \\ \end{array}$

((4))

The proposed transformation (i.e. rotation) is found by taking the SVD of the original motion-sensor matrix, m(t) = U·S·VT, and transforming m(t) into a new matrix: ${\bf{\tilde m}}(t) = {\bf{m}}(t) \cdot {\bf{V}}^{\text{T}}$. ${\bf{\tilde m}}(t)$ is created by concatenating every row of ${\bf{\bar m}}(t)$ in a vector of 3N elements. Furthermore, we have expressed the filter tap weights (k,q) and the three components of the motion sensor m _i (t) in vector form, with T denoting matrix transposition, and where v ₃(t) can be a singular white noise matrix with the covariance matrix Λi,j = qiÅ3δiÅ3,jÅ3I, where Å3 denotes addition modulus 3, δ_i,j is the Kronecker delta, a is a scalar state-transition parameter, and s(t) is the underlying “true” EEG signal, modeled as a white noise with variance λ. We can then recursively estimate the filter taps using the Kalman filter with updated equations (Haykin 2002).

Appendix 2: The Open Hardware and Software Project. The High-Field One System for Real-Time EEG–fMRI

While many commercial and academic systems have been developed to perform EEG recordings during fMRI, rapidly evolving technical, clinical, and scientific requirements have created an opportunity for hardware and software systems that can be customized for specific electrophysiology-fMRI applications. Hardware platforms may require customization to enable a variety of recording types (e.g. electroencephalogram, local field potentials, or multiunit activity) while meeting the stringent and costly requirements of MRI safety and compatibility. Real-time signal processing tools are an enabling technology for electrophysiology-fMRI studies, particularly for application areas such as sleep, epilepsy, neurofeedback, and drug studies, yet real-time signal processing tools are difficult to develop. See the chapter “EEG Quality: The Image Acquisition Artifact” for a discussion of existing hardware solutions. In this section we outline this system, which we call ­High-Field One [i.e. HF-1 (Purdon et al.2008)]. Since high-field MRI is a very challenging environment, it imposes the following requirements: (a) a high dynamic range to avoid saturation during scanning, (b) low RF emissions, and (c) low eddy currents.

RF noise immunity was obtained in HF-1 despite the EEG-MRI requirements of: (1) an absence of ferromagnetic components, (2) resolution of input signals down to 100 nV (exceeding the requirements described in the chapter “The Added Value of EEG–fMRI in Imaging Neuroscience”), and (3) RF noise immunity in the link with the computer system outside the MRI. HF-1 has a bandwidth from DC to 4 kHz (no high-pass filter is needed thanks to the large dynamic range), and a 24-bit sampling rate of 20,833 S/s. It also has a complete set of digital circuits for analogue-to-digital conversion, storage, and USB connection with an external PC. HF-1 is connected to a laptop via a USB optical interface. Furthermore, an optical digital line is used to synchronize EEG acquisition with the PCMCIA digital acquisition card (National Instruments, Austin, TX, USA), enabling us to record the trigger signals from a parallel port of a stimulus PC in order to do real-time averaging of epochs.

Although the system (Fig. 7) has been successfully used at 1.5 and 3 T fields, it was specifically designed for very high fields and was therefore tested on humans and animals at 7 T with the following specifications for the gradient coils: maximum gradient strength 40 mT/m (whole-body) and 60 mT/m (head); slew rate of 200 T/m/s (whole body) and 333 T/m/s (head).

Fig. 7

High-Field One (HF-1) hardware overview. The hardware is organized into three main stages: (1) an amplification system, (2) an analogue-to-digital converter (ADC), and (3) a programmable microcontroller unit (MCU) for controlling ADC functions. The EEG data are relayed outside the MRI via a USB-based optical link. A laptop system is used for data display, recording, integration with external signals such as event triggers and physiological monitoring, and real-time signal processing. The HF-1 hardware is compatible with MRI systems, has been tested at field strengths of up to 7 T, and can be used for both EEG and more general electrophysiological recordings such as local field potential or multiunit activity

Main Design Features

The first stage of the system increases the EEG SNR by amplifying the signals before relaying them to the rest of the system. The purpose of this first stage is twofold: (1) to further attenuate (Aw) the fraction of the RF pulse picked up by the Ink Cap, and (2) to amplify the EEG signal in order to improve its SNR, which is given by:

${\text{SNR}} = \frac{{P^{\text{s}} }}{{P^{\text{n}} + \lambda \rho _1 }},$

((5))

where P ^s is the power of the observed signal (i.e. EEG), λ = (Ri + R)/Ri, Ri is the input resistance of the second-stage amplifier, ,${P^n} = |V_{_{rms} }^{n} |2/(4RB)$ and ρ1 is the intrinsic noise power of the first stage amplifier in the band of interest, B. Hence, the SNR is linearly dependent on the first-stage gain.

The third and last stage (Fig. 7) consists of a microcontroller unit (MCU) that is used to supervise all of the functions of the instruments and the clock management circuit, which generates three clocks: (a) an MCU clock (i.e. 48 MHz), (b) an analogue-to-digital conversion (ADC) clock (i.e. 8 MHz), and (c) a USB clock (i.e. 6 MHz). The MCU synchronises, communicates through a handshake protocol, and controls the input of each ADC. The MCU also controls the internal USB section. The data from the ADC is streamed in a FIFO controller using an internal bus controlled by a line driver. The USB serial port section consists of a USB controller connected to the internal data bus. The USB section is connected to an external custom-shielded USB optical extension. The optical sampling clock section informs the acquisition computer of the sampling frequency and is connected to the MCU; it can be located up to 120 m away and is connected to a DAQ card in the acquisition computer for acquisition of the ERP trigger. A PC runs the Labview code and allows monitoring of the electrophysiological traces in real time. It also performs band-pass filtering, saves this large set of data in real time (Rector and George 2001), and computes steady-state responses and spectrograms, also in real time. Complete synchronisation of the MRI and EEG systems was achieved by generating a 48 MHz clock from the 10 MHz master clock of the Siemens Trio (Siemens AG, Erlangen, Germany) scanner using a direct digital synthesizer.

The HF-1 software and hardware designs are freely available at http://nmr.mgh.harvard.edu/abilab/, subject to a free licensing agreement. The HF-1 hardware system can be constructed based on the complete specifications provided. These specifications include circuit diagrams in Orcad (Cadence, San Jose, CA, USA) format, print circuit board layouts in both Orcad and Gerber (Gerber Systems Corporation) formats, and bills for materials specifying all required components and part numbers. Print circuit board layouts were designed to permit both automated pick-and-place assembly and soldering, as well as hand assembly and soldering. With these specifications, it is possible to achieve turnkey production of the complete hardware system, or components of it, as desired by the end-user.