Jing Xu^{1}, Jingwei Sheng^{1}, Tianyi Qian^{2}, Zihui Su^{3}, and Jia-Hong Gao^{1}

The accuracy of fMRI-constrained EEG/MEG source imaging may be degraded by potential spatial mismatches between the locations of fMRI activation and electrical source activities. To address this problem, we propose a novel fMRI informed time-variant constraint (FITC) method. Simulations were performed to compare the source estimates produced by L2-minimum norm estimation (MNE), fMRI-weighted minimum norm estimation (fMNE), FITC and depth-weighted FITC (wFITC) algorithms with various spatial mismatch conditions. In conclusion, the proposed FITC method is able to better resolve the spatial mismatch problems encountered in fMRI-constrained EEG/MEG source imaging.

Purpose

To develop a more reliable functional neuroimaging technique to achieve high-resolution spatiotemporal mapping of brain activities.^{}The forward solution
of EEG/MEG can be expressed in a simple vector notation:

$$x(t)=Ls(t)+n(t)$$

where x(t) is the EEG or MEG recordings, s(t) is the unknown source strengths, L is an Nx-by-Ns gain matrix and n(t) is the noise vector.

The linear inverse
operator (G) can be expressed as follows^{1}:

$$G= RL^T (LRL^T+C)^{-1}$$

The weights in our proposed FITC method are constructed in a time-variant manner by multiplying the neural electric weights (i.e., $$$R_e$$$) and fMRI weights (i.e., $$$R_f$$$):

$$R(t)=R_f R_e (t)$$

Re can be constructed by taking its diagonal elements to be the MNE results, as follows:

$$R_e (t)=\begin{bmatrix} \hat{s}^{2}_{1}(t) & \cdots & 0\\ \vdots & \hat{s}^{2}_{i}(t) & \vdots\\ 0 & \cdots & \hat{s}^{2}_{N_{s}}(t) \end{bmatrix}$$

where $$$ŝ_i^2$$$represents the estimate source power at location i.

The fMRI weights$$$ R_f $$$will be modified in the case of fMRI missing sources:

$$R(t)=R_{ξ,ρ} R_e (t)$$

$$$R_{ξ,ρ}$$$ is constructed based on two parameters: the normalized
partial area under the curve matrix (i.e.,$$$ρ_i$$$) and the
crosstalk matrix (i.e.,$$$ξ_i$$$) of MNE results^{2}.

We defined a normalized partial area under the curve matrix $$$ρ_i$$$, as follows:

$$ρ_i=\frac{∫_0^Tq_i (t)*ŝ_i^2 (t)dt}{∫_0^Tŝ_i^2 (t)dt}$$

where T is the entire time of interest, and $$$q_i (t)$$$ is an source spatial distribution mask vector at time point t and location i with suprathreshold elements set to 1 and under-threshold elements set to 0. The threshold of $$$q_i (t)$$$ is determined by a t-test between the baseline and task conditions at p < 0.05 with Bonferroni correction.

The crosstalk matrix $$$ξ_i$$$ is defined as follows:

$$ξ_i=\frac{∑_{j≠i}|(G_i L_j )|^2}{|(G_i L_i )|^2}$$

where $$$G_i$$$ is the ith row of G, and $$$L_i$$$ is the ith column of L.

$$$ρ_{ave }$$$ and $$$ξ_{ave }$$$ are the averages of $$$ρ_i$$$ and $$$ξ_i$$$ over the intersection areas of the real fMRI activation regions and significant EEG/MEG response regions, respectively. Locations that are in significant EEG/MEG response regions but not in real fMRI activation regions and meet the conditions that $$$ρ_i$$$ is exceeding $$$ρ_{ave }$$$ and $$$ξ_i$$$ is less than $$$ξ_{ave }$$$ will be defined as the extended activation regions. We set the diagonal elements of $$$R_{ξ,ρ}$$$ corresponding to real fMRI activation regions and the extended activation regions to 1; any other locations we$$$R_{ξ,ρ}$$$ set to 0.1. The off-diagonal elements of $$$R_{ξ,ρ}$$$ were set to 0. The calculating process of FITC is outlined in Fig. 1

Simulations were applied to assess the performance of MNE, fMNE, FITC and depth-weighted FITC (wFITC). We simulated five conditions that are typically encountered in human experiments: match, fMRI missing sources and fMRI extra sources conditions. The EEG data sets were simulated with two different SNRs (3 and 10), and the simulations were repeated 100 times for each condition. When comparing different algorithms, both temporal and spatial accuracies were evaluated. Temporal accuracy is defined as the correlation coefficient between the estimated source waveforms and preset source waveforms . The localized error was defined as the distance between the real dipole location and the most active estimated source location at the time of peak latency. One-way Analysis of Variation (ANOVA) with Tukey’s post-hoc comparisons was applied to test the performance of these four methods.

1. Liu AK, Belliveau JW, Dale AM. Spatiotemporal imaging of human brain activity using functional MRI constrained magnetoencephalography data: Monte Carlo simulations. Proceedings of the National Academy of Sciences, 1998, 95: 8945-8950.

2. Liu AK, Dale AM, Belliveau JW. Monte Carlo simulation studies of EEG and MEG localization accuracy. Human Brain Mapping, 2002, 16:47-62.