Spatiotemporal smoothing for brain-imaging MEG data

Magnetoencephalography (MEG) is a non-invasive technique which measures the electromagnetic activity in the brain by recording the magnetic fields outside the head. Data is acquired by sensitive devices embedded in a helmet placed over the human head. The high temporal resolution of MEG (in the order of milliseconds) is optimal for studying the transient magnetic fields associated with the highly dynamic processes of brain activations. The goal is the identification of spatio-temporal components in the signal that correspond to certain cognitive processes that ideally are carefully manipulated in the respective experiment. Several kinds of noise and artifacts can distort the desired signal. Filtering procedures and averaging across many trials, i.e. replicates of the experiment, are methods usually adopted to summarize the data and increase the signal to noise ratio. However, uncertainty of estimates are usually not taken into account. In this work linear smoothing estimation based on a local fitting approach is applied to smooth the data both in time and space, i.e. the helmet surface, in order to reduce sensor noise. Maps depicting the mean response by smoothing out the sensor noise, plus standard errors for the mean, are produced to help in identifying the time and location where a dipole pattern occurs, which indicates activation. Computational issues are successfully addressed by considering the array representation of the data (Currie et al. 2006). The estimator actually realizes a local mean averaging of the data both over time and space by simply pre-multiplying and post-multiplying the data matrix by a smoothing matrix relative to the space and the time dimension respectively. Standard errors are evaluated by considering, at each time slice, the data as arising from a spatial process, and fitting a covariogram model to the residuals. Analogously, an autoregressive model can be fitted to the residual time series at each sensor. Such a method is helpful in order to address the common case where the sensor noise presents a spatial and temporal structure. The availability of standard errors allows a null hypothesis of null activation to be tested, and maps of t-statistics can be provided to highlight the strength of the detected dipole pattern. The methodology carried out allows single-trial analysis as a useful alternative to the usual practice of averaging raw MEG data from many trials, which usually show a great variability both in phase and amplitude. The benefit of applying moothing estimation at the single-trial level, rather than averaging raw data across replicates, was studied via simulation and also shown in real data examples. Building on this, future research might go in two directions. The first is the development of methodologies which adjust for the trial to trial variability and provide a more effective method of constructing a mean response surface. The second is to consider the multilevel structure of the MEG data in an attempt to model the response by including in the fitting process the variability at the different levels of the hierarchy generated by the experiment (subjects, conditions, trials).