# Localizing fNIRS hemodynamic oscillations on the cortical surface using wavelet Maximum Entropy on the Mean

Edouard Delaire, Jawata Afnan, Shahla Bakian Dogaheh, Jean-Marc Lina, Christophe Grova

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To cite this version:

Edouard Delaire, Jawata Afnan, Shahla Bakian Dogaheh, Jean-Marc Lina, Christophe Grova. Localizing fNIRS hemodynamic oscillations on the cortical surface using wavelet Maximum Entropy on the Mean. 2024 Biennial meeting of the Society of Functional Near-Infrared Spectroscopy (fNIRS 2024), Sep 2024, Birmingham (UK), France. hal-04712662

HAL Id: hal-04712662

https://hal.science/hal-04712662v1

Submitted on 2 Oct 2024

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Distributed under a Creative Commons Attribution 4.0 International License
# Localizing fNIRS hemodynamic oscillations on the cortical surface using wavelet Maximum Entropy on the Mean

Édouard Delaire¹,², Jawata Afnan¹,³, Shahla Bakian Dogaheh¹,²,⁴, Jean-Marc Lina⁵, Christophe Grova¹,²,³

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1. Multimodal Functional Imaging Lab, School of Health, Concordia University, Montréal, Canada
2. Multimodal Functional Imaging Lab, Physics Dpt, Concordia University, Montréal, Canada.
3. Multimodal Functional Imaging Lab, Biomedical Engineering Dpt. and Neurology and Neurosurgery Dpt, McGill, Montréal, QC, Canada
4. Sleep, Cognition, Neuroimaging Lab (SCNLab), Concordia University, Montréal, Canada
5. École de technologie supérieure, Montréal, Canada

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edouard.delaire@concordia.ca

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@EdouardDelaire

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UNIVERSITÉ
Concordia
UNIVERSITÉ

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McGill

## Context

* Hemodynamic signals measured with fNIRS, or fMRI show physiological fluctuations in specific frequency bands, associated with different physiological processes: Cardiac (0.8 - 1.5 Hz), Respiration (0.16 - 0.6 Hz), Low-frequency oscillations (0.04 - 0.15 Hz), Very low-frequency oscillations (0.01 - 0.04 Hz) [1]

* These oscillations are linked to specific physiological and cognitive processes and vary during sleep [2]

* The goal is to investigate and validate the accuracy of reconstructing spontaneous or induced fNIRS oscillations on the cortex.

* The study uses the wavelet Maximum Entropy on the Mean (wMEM) method, developed and recently validated for reconstructing resting state oscillations in EEG/MEG data [3]

* wMEM is an extension of the conventional MEM 3D reconstruction approach which has been previously validated for fNIRS optical tomography [4,5]

* wMEM leverages discrete wavelet representation of fNIRS signals to reconstruct resting state oscillations on the cortical surface for specific frequency bands [6]

## Rationale for using wMEM

**Rationale for using MEM:**

* Sensitive to the **spatial extent** of the underlying generators

* Assume that brain activity is organized in **non-overlapping cortical parcels** that can be switched off

**Rationale for using a wMEM**

* MEM on a **time-frequency representation** of the data

* Better representation of the **temporal structure** of the data

* **Sparse representation** of the data

* Representation of the **transient rhythmic activity**

## Methods

### Maximum Entropy On the Mean (MEM) framework

fNIRS optical tomography problem expressed in the time domain:

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Definition of our reference distribution (prior) $v(J)$:

* Our prior assumes that the brain activity is organized as **K non-overlapping, independent parcels**

* The activity in each parcel is modeled using a **mixture of a Dirac (inactive) and a Gaussian (active)** with mean 0 and spatial covariance $\Sigma_k$.

* The mixture is controlled, for each parcel, using a **hidden variable $\alpha_k$, describing the probability of each parcel being active**

Parcellation of the cortex

Reference distribution $v$:

$$ \prod_{k=1}^{K} ((1 - \alpha_k(t)) \text{Dirac}(0) + \alpha_k(t) \text{Normal}(0_k, \Sigma_k(t))) $$

### Wavelet-Maximum Entropy On the Mean (wMEM) framework

Time-frequency representation of the data:

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Time s

fNIRS optical tomography problem expressed
in the wavelet time-frequency domain: $d_{j,k} = Aw_{j,k} + E$

$$ \left\{ \begin{aligned} q(t) &= \sum_j \sum_k w_{j,k} \psi_{j,k}(t) \\ m(t) &= \sum_j \sum_k d_{j,k} \psi_{j,k}(t) \end{aligned} \right. \quad \text{Discrete wavelet} $$

Noise covariance of $E$ is estimated on the wavelet coefficient for scale 3 (0.6 - 1.25Hz) on baseline data or, if no baseline is available, on surrogate data created by reshuffling the phase of the original signal [3]

Bayesian estimation: Regularization using Entropic technique ensuring a solution that is "close" to our prior distribution, while explaining the data on average.

$v(J)$ (the prior)

$-S_v(p) = KL(p || v)$ (Kullback-Leibler divergence)

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Set of probabilities $p(J)$ that explains the data on average: $A E_{dp}[j] = m$

Scale j

Time s

fNIRS optical tomography problem expressed
in the wavelet time-frequency domain:

Reconstructed Activity at t = 280s

MNE

**Ground Truth (activated Region)**

Reconstructed Activity at t = 280s

MNE

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wMEM

fNIRS Montage

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Simulated time course at 1 dB SNR

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Reconstructed time course

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## Results - Application to real data

### a. Localization of hemodynamic response during motor task (finger tapping)

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Localize then Average
T = 13s

Time course inside the motor region

Average then localize

Localize then Average

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We found similar results when doing the average before or after the 3D localization on the cortex

## Conclusions

* This study demonstrates the ability of wMEM to reconstruct hemodynamic oscillations on the cortex.

* Allowing accurate 3D reconstruction of spontaneous or evoked hemodynamic oscillations on the cortex, allowing the study of task-based experiments or resting state.

* (Soon) Available in Brainstorm / NIRSTORM: https://github.com/Nirstorm/nirstorm

### Evaluation of MNE and wMEM over 61 different activated regions with a SNR of 1 dB or 0.25 dB

SNR: 1 dB

SD (mm)

Correlation

RSA (%)

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SNR: 0.25 dB

SD (mm)

Correlation

RSA (%)

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### b. Estimation of the power spectrum during N2 and N3 sleep

b. Estimation of the power spectrum during N2 and N3 sleep

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We found a similar power spectrum when estimating at the sensor level and on the cortex. The power spectrum on the cortex can better differentiate between N2 and N3 (peak at 0.031Hz)

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## References:

[1] Obrig, NeuroImage, 2000 [2] Ren, Front. Neurol., 2020

[3] Afnan, Neuroimage, 2023 [4] Cai, HBM, 2021 [5] Cai, Sc. Report, 2022

[6] Lina, IEEE TBME, 2014 [7] Fishburn, NeuroImage, 2019

NIRSTORM

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## Funding and acknowledgment:

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NSERC
CRSNG

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CIHR IRSC

Fonds de recherche
Nature et
technologies

Québec

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INNOVATION
Canada Foundation
for Innovation
Fondation canadienne
pour l'innovation

We are thankful to Raymundo Cassani for his help integrating wMEM inside Brainstorm