When There Are No Better Solutions: Characterizing Optimal Communication in the Human Brain Network

1700 

Abstract Submission 

Kayson Fakhar¹, Fatemeh Hadaeghi¹, Caio Seguin², Shrey Dixit¹, Arnaud Messé¹, Bratislav Misic³, Claus Hilgetag^1,4

¹University-Hospital of Hamburg (UKE), Hamburg, Germany, ²Department of Psychological and Brain Sciences, Indiana University, Bloomington, Indiana, ³McGill University, Montreal, Quebec, ⁴Department of Health Sciences, Boston, MA

Kayson Fakhar  
University-Hospital of Hamburg (UKE)
Hamburg, Germany

Fatemeh Hadaeghi  
University-Hospital of Hamburg (UKE)
Hamburg, Germany

Caio Seguin  
Department of Psychological and Brain Sciences, Indiana University
Bloomington, Indiana

Shrey Dixit  
University-Hospital of Hamburg (UKE)
Hamburg, Germany

Arnaud Messé  
University-Hospital of Hamburg (UKE)
Hamburg, Germany

Bratislav Misic  
McGill University
Montreal, Quebec

Claus Hilgetag  
University-Hospital of Hamburg (UKE)|Department of Health Sciences
Hamburg, Germany|Boston, MA

Addressing the human brain as a network unveils its complex connectivity pattern. This network shows a multitude of properties, including an abundance of short-range connections to minimize wiring cost while allowing a small set of long-range connections (Sporns et al., 2004). This set of costly long-range connections provides a shorter network-wide average path-length allowing efficient communication, hence striking a balance between cost and efficiency (Bullmore & Sporns, 2012). However, communication efficiency in this context presupposes brain regions communicate via the shortest path, a notion demanding nodes' global network knowledge (Avena-Koenigsberger et al., 2018). Consequently, alternative communication models (CMs), envisioning signaling via various mechanisms such as random walking and broadcasting have been developed (Seguin et al., 2023). There is yet to be a consensus over how to define communication among brain regions and measure if it is indeed optimal given the structural constraints.

Game theory is a branch of mathematics that studies the strategic interactions of players in a game, assuming that each player aims at maximizing its payoff. For instance, when a buyer and a seller bargain over an item, they both start with extreme proposals that maximize their profit, but their constraints (buyer's budget and the item's selling price) force them to compromise and find a solution that satisfies both parties. Theoretically, for every such a game, there exists a unique equilibrium point where no player can unilaterally increase its payoff. The exact payoff of every player given that division scheme is their "Shapley values" (Gul, 1989; Shapley, 1953). Through multi-perturbation Shapley value Analysis (MSA) (Keinan et al., 2004), we computed the optimal influence (OI) matrix, detailing exact nodal influences at the mentioned equilibrium point. In brief, MSA finds this unique point by exhaustively perturbing every possible combination of nodes and comparing the outcome of each perturbation with others (See Fig1 for more details; Fakhar & Dixit, 2021). Here, we define the game as a large-scale computational model of the human brain dynamics. Specifically, we used the consensus structural connectivity with 219 parcels from the Lausanne dataset and simulated the activity profile of each region by various computational models (linear and nonlinear, including an oscillatory neural mass model). Lastly, to identify which conceptualization of CMs best captures optimal interactions in brain networks, we compared them with the OI matrix using Pearson's correlation.

First, we found that the OI is largely model-independent, as all of our computational models result in the same equilibrium point. This finding suggests that complex neural mass models do not provide extra information compared to simple linear models of information propagation, which are the backbone of graph-theoretical metrics. Second, among the putative CMs, communicability is the most reliable predictor of OI, with r=0.94. By incorporating a broadcasting strategy, communicability considers all path-lengths while exponentially discounting longer walks. However, we found that the exponential discount is too strict for long path-lengths as communicability results in the underestimation of their actual influence. Consequently, we employed a simple analytical model with the same strategy but using a linear discount. This model predicts OI with R2=0.99 (Fig2).

In this work, we employed a game-theoretical framework to, first, provide an intuitive and model-agnostic definition of communication, and, second, to find the optimal point where no node can unilaterally increase its influence over others given the imposed structural constraints. We then compared how much nodes influence each other at this point with other CMs and found that the best fitting ones follow a broadcasting conceptualization that utilizes not only the shortest path but the longer ones as well.

Connectivity (eg. functional, effective, structural) ²

fMRI Connectivity and Network Modeling ¹

Methods Development

Computational Neuroscience

Cortex

Data analysis

FUNCTIONAL MRI

Informatics

Modeling

NORMAL HUMAN

Open-Source Code

Open-Source Hardware