LEiDA

202211211750
Status:
Tags: 1-Year Crash Course in Computational Neuroscience fMRI Connectomics

Leading Eigenvector Dynamics Analysis

LEiDA is a framework to simulate possible metastable substates from fMRI data, based on Cabral2017. In summary, LEiDA characterizes the temporal evolution of dynamic functional connectivity (dFC, FCD) based on fMRI phase-coherence connectivity (with reduced dimensionality)

Type of dynamic functional connectivity

GitHub

Papers

• Original: Cognitive performance in healthy older adults relates to spontaneous switching between states of functional connectivity during rest
• Kringelbach’s interpretation on Carhart-Harris psilo data:

Using LEIDA

conda create --name pL python=3.9
conda activate pL
 
pip install pyleida

The toolbox was designed to take away as much pain as possible. Complete pipeline & exploration of results can be easily performed with only the LEiDA class.

1. Create a folder with necessary files/data (see more on GitHub)
   • BOLD time series
   • Metadata
   • ROIs
   • Parcellations
2. Run the analysis:

# Import the Leida class
from pyleida import Leida
 
# Instantiate the Leida class, specifying where our data is located
ld = Leida('data')
 
# Run the complete pipeline:
# Here, 'TR' specifies the Time Repetition of the fMRI data,
# 'paired_test' specifies whether the groups/conditions are
# independent or related, and 'n_perm' the number of permutations
# that will be used in the statistical analyses.
ld.fit_predict(TR=1.433,paired_tests=False,n_perm=5_000,save_results=True)

1. Explore the methods of the Leida object to explore results, generate additional figures and contents
   • Examples are in the Github repo

Math

Lord2019

1. Perform BOLD Phase-locking analysis
   • The leading eigenvector $V_1(t)$ is a low-dimensional representation of the BOLD phase-locking patterns over time.
2. Extract leading eigenvector → reduce dimensionality of $dPL$ (tensor) matrix from NxNxT to Nx1 vector which captures main orientation of BOLD phases over all areas, where each element in $V_1(t)$ represents the projection fo the BOLD phase in each brain area into the leading eigenvector.
   • Direction of elements →clusters (1 or 2)
   • Magnitude of each element → ‘strength’ with which brain areas belong to the communities they’re in
3. Identify recurrent phase-locking patterns using a clustering algorithm (e.g. k-means, hidden markov model)
   • divides pool of data points into predefined number of clusters $k$.
   • Each cluster is represented by a central vector, which represents a recurrent BOLD phase-locking pattern (PL state)
   • 5-10 $k$ clusters should be used, covering range of functional networks commonly reported in resting-state fMRI literature (Yeo et al., 2011)
   • k-means clustering returns $k$ cluster centroids in shape of Nx1 vectors $V_c$ representing average vector of each cluster → these correspond to PL states
   • clusters can be rendered onto cortical surface with HCP workbench
   • PL states can be represented back into matrix format (NxN) by computing outer product $V_c\ast V_c^t$ (matrix rank 1) with positive values between all elements with same sign in $V_c$ and negative values between elements of different signs
4. Evaluate probability of occurrence and switching profiles of PL states
   • Assigned to each TR is a single PL state (select closest centroid $V_c$ at each TR)
   • Calculate probability with state time courses (number epochs assigned to given PL state divided by total number epochs in each scanning session)
   • Calculate difference in probabilities of occurrence before and after injection
     • Compare with a paired t-test (permutation-based?)
5. Compare with resting-state networks
   • Transform RSNs (Yeo et al., 2011) into vectors with 90 elements each, where each element scales contribution of AAL brain area to corresponding RSN
   • Compute bivariate correlation with centroid vectors where all negative elements in $V_c$ are zero
6. Evaluate global order and metastability
   • Degree of order between BOLD phases at each timepoint can be quantified with Kuramoto Order Parameter OP(t) (range 0-1)
   • $OP(t)=\frac{1}{N}|{\sum }_{n-1}^N{e}^{i\theta (n,t)}|$
   • Mean magnitude of OP describes incoherence, partial synchronicity, or full synchronicity (Deco and Kringelbach, 2016)
   • Standard deviation of OP → degree of metastability in system (Cabral et al., 2014b)

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References