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Extracting the Multiscale Causal Backbone of Brain Dynamics

Gabriele D'Acunto, Francesco Bonchi, Gianmarco De Francisci Morales, Giovanni Petri

TL;DR

This work proposes the multiscale causal backbone of brain dynamics, shared by a set of individuals across multiple temporal scales, and devise a principled methodology to extract it, and analysis of individual multiscale causal structures confirms the existence of a causal fingerprint of brain connectivity.

Abstract

The bulk of the research effort on brain connectivity revolves around statistical associations among brain regions, which do not directly relate to the causal mechanisms governing brain dynamics. Here we propose the multiscale causal backbone (MCB) of brain dynamics, shared by a set of individuals across multiple temporal scales, and devise a principled methodology to extract it. Our approach leverages recent advances in multiscale causal structure learning and optimizes the trade-off between the model fit and its complexity. Empirical assessment on synthetic data shows the superiority of our methodology over a baseline based on canonical functional connectivity networks. When applied to resting-state fMRI data, we find sparse MCBs for both the left and right brain hemispheres. Thanks to its multiscale nature, our approach shows that at low-frequency bands, causal dynamics are driven by brain regions associated with high-level cognitive functions; at higher frequencies instead, nodes related to sensory processing play a crucial role. Finally, our analysis of individual multiscale causal structures confirms the existence of a causal fingerprint of brain connectivity, thus supporting the existing extensive research in brain connectivity fingerprinting from a causal perspective.

Extracting the Multiscale Causal Backbone of Brain Dynamics

TL;DR

This work proposes the multiscale causal backbone of brain dynamics, shared by a set of individuals across multiple temporal scales, and devise a principled methodology to extract it, and analysis of individual multiscale causal structures confirms the existence of a causal fingerprint of brain connectivity.

Abstract

The bulk of the research effort on brain connectivity revolves around statistical associations among brain regions, which do not directly relate to the causal mechanisms governing brain dynamics. Here we propose the multiscale causal backbone (MCB) of brain dynamics, shared by a set of individuals across multiple temporal scales, and devise a principled methodology to extract it. Our approach leverages recent advances in multiscale causal structure learning and optimizes the trade-off between the model fit and its complexity. Empirical assessment on synthetic data shows the superiority of our methodology over a baseline based on canonical functional connectivity networks. When applied to resting-state fMRI data, we find sparse MCBs for both the left and right brain hemispheres. Thanks to its multiscale nature, our approach shows that at low-frequency bands, causal dynamics are driven by brain regions associated with high-level cognitive functions; at higher frequencies instead, nodes related to sensory processing play a crucial role. Finally, our analysis of individual multiscale causal structures confirms the existence of a causal fingerprint of brain connectivity, thus supporting the existing extensive research in brain connectivity fingerprinting from a causal perspective.
Paper Structure (16 sections, 2 theorems, 14 equations, 18 figures, 1 table, 1 algorithm)

This paper contains 16 sections, 2 theorems, 14 equations, 18 figures, 1 table, 1 algorithm.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. Learning individuals multiscale DAGs
  4. Learning the multiscale causal backbone
  5. Empirical assessment on synthetic data
  6. Analysis of resting-state fMRI data
  7. Conclusion and future work
  8. Proof of Lemma \ref{['lem:waveletgauss']}
  9. Computational cost
  10. Hyper-parameters
  11. Metrics
  12. Additional results
  13. Synthetic data
  14. Analysis of the cardinality of individual multiscale DAGs
  15. Comparison with baselines and analysis of the resulting MCBs by scale
  16. ...and 1 more sections

Key Result

Lemma 1

The wavelet coefficient $\tilde{x}_i^{s,j}[n]$ is distributed according to a zero-mean Gaussian distribution, for all $s \in [S], \, j\in [J], \text{ and } n \in [N]$.

Figures (18)

  • Figure 1: Raincloud plots of the distributions of (left) F1 score and (right) SHS, obtained by the tested methods over $50$ synthetic data sets. For readability, we omit the results by DTF and PDC.
  • Figure 2:
  • Figure 3: Rain plots depicting the (left) F1 score and (right) SHS, obtained by the considered methods over $50$ synthetic data sets.
  • Figure 4:
  • Figure 5: Connectivity backbones retrieved by the considered baseline methods for the left hemisphere. ROIs numbering in \ref{['tab:numbering']}.
  • ...and 13 more figures

Theorems & Definitions (10)

  • Lemma 1
  • proof
  • definition 1: Multiscale linear DAG for the $s$-th individual
  • definition 2: $p$-persistent arc
  • definition 3: Candidate universe
  • definition 4: Set of idiosyncratic causal arcs
  • definition 5: Multiscale causal backbone, MCB
  • remark 1
  • Lemma 1
  • proof