Characterizing cognitive brain networks using group-level statistical inferences of information-based measures

School Lyon - 22/10/2021

Etienne Combrisson - Postdoc BraiNets' team INT Marseille

# Program of the day

  1. Overview of the Frites software : what it is for, what can you do with it etc.
  2. Presentation of the sEEG data
  3. Data management : data formatting, data selection, input / output types etc.
  4. Measuring information : linking brain data to an external variable (stimulus types, behavior etc.)
  5. Statistics : group-level statistics, fixed- and random-effect models, non-parametric statistics, correction for multiple comparisons etc.
  6. Functional connectivity : directed and undirected functional connectivity, task-related functional connectivity etc.
  7. Application to your data

30min

1h30min

1h

1h

30min

My very optimistic program !

Frites

# Open-source Python software

[FRITES] Framework for Information Theoretical analysis of Electrophysiological data and Statistics

Vinicius Lima Cordeiro

INT/INS, Marseille

# Shout out to main Frites' contributors

# Aim of the software : big picture

Brain data

Information Framework

Task-related functional (un)directed connectivity

Local task-related

brain activity

Group-level statistical inferences

Extract dynamic spatiotemporal cognitive brain networks in relation to cognitive processes

# Aim of the software : in depth

Inputs

Local measures
power, phase, PAC etc.
Connectivity estimations
(d)FC, (un)directed
Graph-measures
degree, modularity, associativity etc.

Link with external variable

(IT)

Contrasting conditions

"classification" like

  • baseline vs. task
  • stimulus A vs. B
  • Reaction time (RT)
  • Learning model
  • Prediction error
Regression

"correlation" like

Removing influence

"partial-correlation" like

  • RT | {easy, hard}

Group-level statistics

Measure of information

"Conjunction"
#subjects significant
Fixed-effect
case studies
Random-effect
generalization

# Structure of the software

  1. frites.dataset = data containers
    • LFP / connectivity / PSD / TF maps etc.
    • Single / Multi subjects & Single / Multi sessions
  2. frites.workflows = computations performed on datasets
    • Workflow of information (frites.workflows.WfMi)
    • Workflow of statistics (frites.workflows.WfStats)
  3. frites.conn = metrics of dynamic functional connectivity
    • Undirected connectivity (frites.conn.conn_dfc)
    • Directed connectivity (frites.conn.conn_covgc)
  4. Others 
    • frites.estimator = home-made and custom information-based estimators (information-theory, machine-learning etc.)
    • frites.simulations = create artificial simulated data
    • frites.utils = utility functions (e.g. data smoothing)

# Typical framework

Data

Results

Task variable

  • Categorical variable
    • Stimulus type
    • Experimental condition
  • Continuous variable
    • Behavioral model (PE, surprise)
    • Reaction time

Brain data

  • LFP, connectivity, spikes, power, TF maps etc.
    • Single / Multi subjects
    • Single / Multi sessions
    • Single / Multi brain regions

Effect size

  • Per brain region / electrode
  • Dynamic (per time point if there's a time axis)
  • Per or across a population (i.e. across subjects or sessions)

P-value

  • Same dimension as the effect size
  • Corrected for multiple-comparisons

Statistics

frites.workflows
WfStats

Corrected p-value

  • Effect significantly differ from chance?
  • Correct for multiple comparisons (time, space etc. e.g. using cluster-based)
  • P-value inference

Information

frites.workflows
WfMi

Measure of effect size

  • Linking the brain data to the task variable (I(x; y))
  • Provide a measure of effect size
    • ​Per / across subjects
    • Per / across sessions

Dataset

frites.dataset
DatasetEphy

Merge group data

  • x = brain data
  • y = task variable
  • Checking data properly formatted
  • Data conversion

Data presentation

# sEEG data and Probabilistic Learning Task

17 subjects with a pharmaco resistant epilepsy implanted with intracranial electrodes 

[REW] Reward condition

[PUN] Punishment condition

# Four cortical regions involved during learning

Inside each brain region, there is multiple recording sites (i.e. channels / contacts) coming from multiple subjects (potentially different)

# Data organisation

[anat] Single subject excel files containing anatomical informations. Two columns : 

  • contact : name of the recording contact
  • roi : (region of interest) name of the brain region

[beh] Single subject excel files containing behavioral informations. Five columns : 

  • valence : outcome valence (+1€, +0€, -0€, -1€)
  • code : conventional integer (2, 1, -1, -2)
  • block : block design (series of stimuli)
  • RT : reaction time
  • PE : Prediction Error (learning model)

[hga] Single subject high-gamma activity (HGA). The data are saved as 3D arrays (n_epochs, n_channels, n_times)

# Open questions

  1. Can we find differences of high-gamma activity (HGA) during the reward condition (i.e contrasting +1€ vs. +0€)?
  2. Can we find differences of HGA during the punishment condition (i.e contrasting -1€ vs. -0€)?
  3. Can we find brain regions for which the HGA is correlated with the reaction time (RT)?
  4. Can we find brain regions for which the HGA is correlated with the prediction error (PE) during the reward or punishment condition?

I/O

# Data preparation

  • "What are the input types supported by Frites?"
  • "What is the output type of Frites' functions?"

Let's talk about how your data should be formatted to start using Frites

# Frites' inputs / outputs

INPUTS

OUTPUTS

# Why using xarray?

-1

-0.75

-0.5

-.025

0.

0.25

0.5

0.75

1.

1.25

3.

3.25

3.5

3.75

4.

4.25

4.5

4.75

5.

5.25

Times (seconds)

e1

e2

e3

e4

e5

e26

e27

e28

e29

e30

Electrodes

s1

s1

s1

s2

s2

s10

s10

s11

s11

s11

Subjects

Baseline

Period of interest

# Xarray = labelled NumPy array

Your data

Labelling

Labelling layer on top of your data to facilitate data selection and overall manipulations

# Data selection : NumPy vs. Xarray

"Select the neural activity during the baseline of subject 10, electrode 26"

# data.shape = (n_electrodes, n_times)

# select the electrode of the subject
is_subject = subject_names == 's10'
is_elec = elec_names == 'e26'
is_both = np.logical_and(is_subject, is_elec)

# select baseline activity
is_baseline = times < 0.

# apply selection to the data
data_n = data[is_both, is_baseline]
# data.shape = (n_electrodes, n_times)
# assuming that data is already an DataArray
 
data_n = data.sel(
  subject='s10',
  elec='e26',
  times='baseline'
)

# NumPy ↔ Xarray

NumPy → Xarray

Array labelling

import numpy as np
import xarray as xr

"""
raw.shape = NumPy array (n_electrodes, n_times)
elec_names = vector of electrode names (n_electodes,)
time_vec   = time vector (n_times,)
"""

raw_xr = xr.DataArray(
  raw,                           # NumPy array of data
  dims=('electrodes', 'times'),  # dimension names
  coords=(elec_names, time_vec)  # coordinates values
)

Xarray → NumPy

Drop labelling

import numpy as np
import xarray as xr

"""
raw_xr.shape = Xarray DataArray (n_electrodes, n_times)
elec_names = vector of electrode names (n_electodes,)
time_vec   = time vector (n_times,)
"""

# retrieve coordinates
elec_names = raw_xr['electrodes'].data
time_vec = raw_xr['times'].data

# get the raw data as a NumPy array
raw = raw_xr.data

# Scratching the surface of Xarray

Advantages of using Xarray

  • Very clean and readable way to select to brain data !
  • Save / load your data with the labels !
  • Add attributes to your data (sampling frequency, experimental details etc.). Nice for sharing self contained files !
  • many, Many, MaNy, MANY operations supported !
# maximum / minimum and mean across time points
data.max('times')
data.min('times')
data.mean('times')

# operations on groups
data.groupby('brain_regions').mean('brain_regions')
data.groupby('time_period').mean('time_period')

# add attributes
data.attrs['sampling_frequency'] = 1024.
data.attrs['session'] = 1
data.attrs['animal'] = 'rat_1'

# save and reload your data
data.to_netcdf('my_data.nc')
data = xr.open_dataarray('my_data.nc')

Limitations of Xarray

  • There's a learning curve (definitly)
  • Black box operations
  • Documentation is not "neuro" oriented

# Coding : time to play with Xarray

Datasets

# Definition

frites.dataset.DatasetEphy

Container of brain data for then performing computations either on a single subject or on a population (i.e. to find reproducible effects across participants or sessions)

# Definition of a DatasetEphy

## Merging multiple participants

from frites.dataset import DatasetEphy

dt = DatasetEphy([raw_s1, raw_s2, raw_s2, raw_s3, raw_s4])
DatasetEphy([             ])

## Input type for each participant

=          |                   |

## Input shape for each participant

3D epochs data

  • Raw = (n_epochs, n_electrodes, n_times)
  • Power = (n_epochs, n_roi, n_times)
  • PSD = (n_epochs, n_electrodes, n_frequencies)
  • Conn = (n_epochs, n_connections, 1)

4D epochs data

  • TF = (n_epochs, n_electrodes, n_frequencies, n_times)
  • CFC = (n_epochs, n_roi, n_phases, n_amplitudes)
  • Coh = (n_epochs, n_connections, n_frequencies, n_times)

# Coding : time to play with Xarray

Measuring

information

# Measures of information

Brain data
Power, spiking rate, functional connectivity etc.

Brain data

Measure of information
Reflects how much brain data carry information about the task (Kriegeskorte et al. 2006)

Task-variables and behavior

Discret stimulus, outcomes

Continuous psychometrics
Reaction times
Continuous behavioral models
Prediction error, Surprise

# Popular providers of measures of information

Information-based measures : how much a neural signal or a link between brain regions carry information about the task (Kriegeskorte et al., 2006)

  • Gaussian-Copula Mutual Information (GCMI, Ince et al. 2017)
    • Great sensibility, noise resistance
    • Bias-corrected (#number of trials per conditions)
    • Computationally inexpenssive (i.e fast !)
    • Monotonicity assumptions
  • Possibility to extend to other measures of information
    • ML metrics
    • Correlations (Pearson, Wilcoxon etc.)
    • Measure of distance (e.g distance correlation)
Information-theory (IT)
Mutual-information, entropy
Model-free
Machine-learning (ML)
Classifiers, regressions
Model-based

# Default metric used in Frites and conventions

  • Gaussian-Copula Mutual Information (GCMI, Ince et al. 2017)
    • Great sensibility, noise resistance
    • Bias-corrected (#number of trials per conditions)
    • Computationally inexpenssive (i.e fast !)
    • Monotonicity assumptions

mi_type='cd'

  • brain data = continuous
  • variable   = discrete

mi_type='cc'

  • brain data = continuous
  • variable   = continuous

Contrasting conditions

Quantifying how much the brain activity differs between 2 (or more) conditions

Stimulus A vs. Stimulus B; Baseline vs. Outcome etc.

Correlation-like

"Correlate" brain activity with a continuous variable

Learning curve, contingency, surprise, prediction error etc.

# Coding : let's measure information

Statistics

# Overview of the statistics used in Frites

Three important points

  1. The goal of Frites is to being able to draw statistical inferences either at the single-subject level or at the population-level
  2. We are combining measures of information and non-parametric statistics
  3. The p-values can be corrected at several levels (test-wise or cluster-wise)

Combrisson, E., Allegra, M., Basanisi, R., Ince, R. A., Giordano, B., Bastin, J., & Brovelli, A. (2021). Group-level inference of information-based measures for the analyses of cognitive brain networks from neurophysiological data. under review + biorxiv

# Statistical inferences on a population

What does population mean?

  • Goal : find effects that are present at the population level
  • Problem : how to take into account the inter-subjects / sessions / contacts variability?
Several subjects
Several sessions from a single subject
Several recording sites in a single brain region

# Group-level statistics on information-based measures

Single-participant

Fixed-Effect

Random-Effect

Quantitative statistics

How many participant / contacts / sessions have the effect?

Typical characteristics of the population of participants

  • Requires lower #participants
  • Great power
  • Reproducible effect
  • Can't generalize

Average characteristics of the population of participants

  • Can generalize
  • Adapt to inter-subject variability
  • Requires higher #participants
  • P-values : inferred using permutation-based non-parameteric statistics + cluster-based correction for multiple-comparisons
  • RFX : model of the population is flexible (participants / sessions / contacts)

Friston et al., NeuroImage (1999);  Maris and Oostenveld, 2000; Giordano et al., 2017; Combrisson et al. in prep

# Coding : let's play with statistics

Functional

connectivity

# Connectivity metrics : undirected amplitude correlation

Static functional connectivity
Contact 1
Contact 2
Times
Dynamic functional connectivity
Contact 1
Contact 2

# Connectivity metrics : covariance-based Granger causality

I(roi_1past; roi_2present | roi_2past)

ROI 1

ROI 2

Static covGC

times

Dynamic covGC

# Coding : let's measure connectivity

Real data

application