An F-ratio-based method for estimating the number of active sources in MEG

Abstract

Introduction: Magnetoencephalography (MEG) is a powerful technique for studying the human brain function. However, accurately estimating the number of sources that contribute to the MEG recordings remains a challenging problem due to the low signal-to-noise ratio (SNR), the presence of correlated sources, inaccuracies in head modeling, and variations in individual anatomy.

Methods: To address these issues, our study introduces a robust method for accurately estimating the number of active sources in the brain based on the F-ratio statistical approach, which allows for a comparison between a full model with a higher number of sources and a reduced model with fewer sources. Using this approach, we developed a formal statistical procedure that sequentially increases the number of sources in the multiple dipole localization problem until all sources are found.

Results: Our results revealed that the selection of thresholds plays a critical role in determining the method's overall performance, and appropriate thresholds needed to be adjusted for the number of sources and SNR levels, while they remained largely invariant to different inter-source correlations, translational modeling inaccuracies, and different cortical anatomies. By identifying optimal thresholds and validating our F-ratio-based method in simulated, real phantom, and human MEG data, we demonstrated the superiority of our F-ratio-based method over existing state-of-the-art statistical approaches, such as the Akaike Information Criterion (AIC) and Minimum Description Length (MDL).

Discussion: Overall, when tuned for optimal selection of thresholds, our method offers researchers a precise tool to estimate the true number of active brain sources and accurately model brain function.

Keywords: AIC; Alternating Projection (AP); F-ratio; MDL; MEG; source enumeration; source localization.

Figure 1

Flowchart of the F-ratio method for estimating the number of sources.

Figure 2

Accuracy (%) of the F-ratio method for estimating the number of active MEG sources (on vertical axis) under different threshold values (on horizontal axis). Performance evaluation was conducted across various experimental conditions: (A–C) varying number of true sources Q, (D–F) SNR levels from -8 to 8 dB, (G–I) inter-source correlation values ρ from 0.1 to 0.9, (J–L) different model errors, and (M–O) different cortical anatomies. Each experimental condition was tested using 100 Monte-Carlo repetitions to ensure statistical robustness. To account for head registration errors, we incorporated inaccuracies into the lead field matrix by applying a translation of 1mm posterior (X-axis), rightward (Y-axis), and upward (Z-axis).

Figure 3

Optimal F-ratio threshold values, adjusted for the signal-to-noise ratio (SNR) level and the number of active sources in the MEG data.

Figure 4

Performance of adjusted F-ratio thresholds in simulated data. The thresholds were optimized for Anatomy 1 and applied to three different anatomies (Anatomies 2, 3, and 4). The F-ratio method was employed to estimate the number of sources under varying levels of source correlation (A) ρ = 0.1, (B) ρ = 0.5, and (C) ρ = 0.9, while maintaining a signal-to-noise ratio of 0 dB.

Figure 5

Comparison of the F-ratio, AIC, and MDL methods in simulated data for estimating the true number of dipoles at various SNR levels: (A) SNR = -8 dB, (B) SNR = -4 dB, and (C) SNR = 4 dB, and different levels of source correlation: (D) ρ = 0.1, (E) ρ = 0.5, and (F) ρ = 0.9.

Figure 6

Performance of F-ratio method in phantom data. (A) Real phantom provided by the MEG vendor MEGIN (Taylor et al., 2016). (B) Location of the 32 artificial dipoles of the MEGIN phantom. (C) Example sensor measurements from two active dipoles with a temporal delay of 29 ms, following temporal and spatial prewhitening, corresponding to SNR 5.5 dB. (D) Performance of F-ratio method in estimating the number of active dipoles.

Figure 7

Performance of the F-ratio method in estimating the number of sources in human auditory data. (A) Comparison of obtained F-ratio values in human data with optimal F-ratio thresholds, supporting a model with two active sources. (B) Plot of the sum of squares of residuals for models with different numbers of active sources. (C) Localization of a single source. (D) Localization of two sources. (E) Localization of three sources.