BOLD Phase-locking analysis

202211211601
Status:
Tags: fMRI LEiDA Connectomics

The first step of LEiDA is to compute the phase alignment between pairs of BOLD parcellation map regions.

1. Estimate BOLD phases $\theta (n,t)$ with Hilbert transform for each BOLD regional timecourse
   • Expresses a given signal $x$ as $x(t)=A(t)\ast cos(\theta (t))$
   • $A$ = time-varying amplitude
   • $\theta$ = time-varying phase
   • Represented over one area $n$ over time $e^{i\theta (t)}$, where $sin(\theta (t))$ represents the imaginary part of the analytic phase and $cos(\theta (t))$ represents the real part.
   • $cos(\theta (t))$ captures the oscillatory dynamics of the BOLD signal
2. Generate dynamic phase-locking matrix dPL(n,p,t) which estimates phase alignment between each pair of brain areas $n$ and $p$ at each time $t$:

$dPL(n,p,t)=cos(\theta (n,t))-\theta (p,t))$

Because of the cosine function, two areas $n$ and $p$ with (temporarily) aligned BOLD signals at a given TR will have a phase-locking value = 1. Opposite phase differences, of course, are -1.

$dPL$ is a 3D tensor with size NxNxT.

Example of BOLD phase-locking analysis

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