Cost-Reference Particle Filter-Based Method for Constructing Effective Brain Networks: Application in Optically Pumped Magnetometer Magnetoencephalography

Optically pumped magnetometer magnetoencephalography (OPM-MEG) represents a novel method for recording neural signals in the brain, offering the potential to measure critical neuroimaging characteristics such as effective brain networks. Effective brain networks describe the causal relationships and information flow between brain regions. In constructing effective brain networks using Granger causality, the noise in the multivariate autoregressive model (MVAR) is typically assumed to follow a Gaussian distribution. However, in experimental measurements, the statistical characteristics of noise are difficult to ascertain. In this paper, a Granger causality method based on a cost-reference particle filter (CRPF) is proposed for constructing effective brain networks under unknown noise conditions. Simulation results show that the average estimation errors of the MVAR model coefficients using the CRPF method are reduced by 53.4% and 82.4% compared to the Kalman filter (KF) and maximum correntropy filter (MCF) under Gaussian noise, respectively. The CRPF method reduces the average estimation errors by 88.1% and 85.8% compared to the MCF under alpha-stable distribution noise and the KF method under pink noise conditions, respectively. In an experiment, the CRPF method recoversthe latent characteristics of effective connectivity of benchmark somatosensory stimulation data in rats, human finger movement, and auditory oddball paradigms measured using OPM-MEG, which is in excellent agreement with known physiology. The simulation and experimental results demonstrate the effectiveness of the proposed algorithm and OPM-MEG for measuring effective brain networks.