Notes for the tutorial: Fieldtrip Neuronal Osciallation and Synchrony

Different tapers have different leakage profile. The simplest taper is a Boxcar taper, which cut offs everything for some specific values and only leave the values within a certain range. The spectral leakage profile for the Boxcar taper is pretty bad - many frequencies near the target frequency are contributing to the power. A Hanning taper or Gaussian taper is attenuating the the contribution of the frequencies further away (side lobes) from the target frequency while having a wider main lobe.

A multitaper method is applied to smooth the frequency power ususally used in more high frequency range. It can smooth the high frequency powers that usually contain high variance across trials and hard to obtain statistical significance. The smoothing smooth a single frequency into a range of frequency, e.g., if our target frequency is 30Hz, then a 8 taper smoothing frequency gives a frequency range from 22Hz to 38Hz (still need to look into why this is the case). Multitapering is a common technique to control spectral leackage.

For low frequency, using a Hanning taper is good enough. Using too many tapers will smooth all the important signals in lower frequencies. The example gives in the video is that from 1-30Hz, Hanning, from 30Hz and above, use ‘dpss’ multitapering.

Brain signal is not stationary. That’s why we need time-frequenct analysis. There is a trade off between time resolution and frequency resolution. In general, if you want a better frequency resolution, you end up with a worse time resolution.

Wavelet is similar to Fourier, by applying convolution of wavelet components that capture different frequencies. A wavelet is a sine or cosine wave convolve with a taper. The only parameters that we can tune is the length of the wavelet - the number of cycles we use in the wavelet signal, usually use 5 (3 for lower frequencies and 7 for higher frequencies).

This is some example code working with Fourier and Wavelet in Fieldtrip:

Notes for the tutorial: Source reconstruction using beamforming techniques

Source reconstruction methods:

1. Single and multiple (point like) dipole models
   • Assume a small number of sources
   • Where (& how many) are strongest source
2. Distributed dipole models
   • Assume activity everywhere
   • What is the distribution of activity over the brain
3. Spatial filtering
   • Assume that the time-courses of different sources are uncorrelated
   • What is the amount of activity at a given brain location

Use multitapers to smooth the frequency spectrum, and get the targeted time window and the frequency range. Multitapering - increase frequency smoothing without changing length time window.

The beamformer (LCMV & DICS) are source localization methods for time domain signals and frequency domain signals using spatial filtering. This method estimate the source activity on every point of a grid, find a matrix that maximize the variance of the target source point and minimize that for the others. (Will need to follow up with the original papers for LCMV and DICS).

This post a review of the paper: Introduction to the Foundations of Causal Discovery. (Eberhardt, 2017)

Causal relationships are important because it shows us how a system behaves under intervention. A causal relationship is usually studied under an experimental setting such as a randomized controlled trial “each individual in the experiment is randomly assigned to either the treatment or control group”. A randomized controlled trial gets rid of the effects of confound variables that are the common causes of the targeted variables. A do operator is introduced $p(y|do(x))$ to distinguish the interventional conditional probability from the observational conditional probability $p(y|x)$.

(To be continued…)

Eberhardt, F., 2017. Introduction to the foundations of causal discovery. Int J Data Sci Anal 3, 81–91. https://doi.org/10.1007/s41060-016-0038-6

I have some ideas recently that is it possible to study the brain, coming up with a new theory/explaination of neural mechanism by running simulations using the recent deep neural network framework. Also, if possible, when we combine the Bayesian graphical models and causal learning, can we explain more about how the brain works?

This post is a summary of the paper: Spectral Spatiotemporal Imaging of Cortical Oscillations and Interactions in the Human Brain (Lin et al., 2004)

A Computationally Efficient Source Estimation Algorithm that Localizes cortical oscillations and their phase relationships.

This paper proposed a method to do source estimation that localizes cortical oscillations and their phase relationships.

(1) It creates a map of the cortical oscillations on the cortical surface

(2) It is able to detect rapidly changing power and phase relations

(3) It can combine prior information from other functional imaging techniques such as fMRI

The signal is firstly processed by a band-pass filter, then use a cortically constrained minimum norm estimate (MNE) that mentioned in a previous blog. The phase-locking value is also calculated using the source converted signal.

It is worth to mention that the source estimation algorithm here (the MNE) is demonstrated a lot more clear than the original paper (Hamalainen).

The source covariance matrix incorporates a priori assumption on the spatial distribution of the source currents… MNE is known to have a bias towards superficial currents, caused by the attenuation of the MEG lead fields with increasing source depth.

Therefore, a correction is made to scale the A matrix, the gain matrix, which is the solution of the free source orientation forward problem

… thus having three columns for each source location, representing the solution according to each orthogonal direction.

After the wavelet transformation, the matrix obtained from source estimation is applied to each channel and the time-varying power and synchronization (PLV) can be computed. After complex wavelet transformation and applying the source estimation matrix, we get a time series of complex signals. The power is getting the amplitude of the complex signal. Here the source synchronization is done using a reference channel (seed method).

Reference

Lin, F.-H., Witzel, T., Hämäläinen, M.S., Dale, A.M., Belliveau, J.W., Stufflebeam, S.M., 2004. Spectral spatiotemporal imaging of cortical oscillations and interactions in the human brain. NeuroImage 23, 582–595. https://doi.org/10.1016/j.neuroimage.2004.04.027

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