A Novel Method to Investigate Neurodevelopment Using Ising Temperature and Graph Neural Networks

1242 

Abstract Submission 

Rodrigo Carvalho¹, Walter Pinaya², João Sato¹

¹Federal University of ABC, São Bernardo do Campo, São Paulo, ²King's College London, London, London

Rodrigo Carvalho  
Federal University of ABC
São Bernardo do Campo, São Paulo

Walter Pinaya  
King's College London
London, London

João Sato  
Federal University of ABC
São Bernardo do Campo, São Paulo

One of the biggest challenges in neuroscience is comprehending brain function mechanisms on different temporal and spatial scales. In particular, the topic of neurophysiology during the resting state at the macroscopic level is of great interest, not only in contribution to neurodevelopment and psychiatry but also to emergent patterns that microscopic components cannot explain. Recent studies show that brain dynamics may be modelled by lattice models near criticality, such as the 2D Ising Model [1,2]. The Ising temperature, which is the order parameter dictating the phase transitions of the model, is being used to better understand different brain states [3,4]. This work aims to investigate neurodevelopment through a novel method to estimate the Ising Temperature of the brain from functional Magnetic Resonance Imaging (fMRI) data using functional connectivity and Graph Neural Networks (GNNs) trained with Ising Model networks.

The Attention Deficit Hyperactivity Disorder 200 (ADHD200) dataset (491 healthy subjects, 285 subjects with ADHD, 7–21 years, M = 11.99, SD = 3.2 years) was used. The functional connectivity graphs of the whole brain were calculated by Pearson's correlation of the 190 ROIs. The 2D Ising model was simulated using a lattice of 330x330 spins fluctuating over 200 time steps after thermal equilibrium, where each time step gives all the spins of the lattice the opportunity to change their state. Then, the lattice is averaged over blocks of 23x23 spins, in order to get a continuous time series representative of the fMRI signal. The 2D Ising Model graphs were calculated by Pearson's correlation, resulting in 190 nodes. To prepare the graphs for the GNN, the edges were selected by a 10-nearest-neighbours algorithm using the FC matrix, each node represented a ROI and the node features were the connectivity with the other ROIs [5]. To calculate the Ising Temperature for the brain networks, a GNN was trained, with 3 graph convolutional layers, a global average pooling process, and 2 linear layers. The activation function was Leaky-ReLu, the dropout technique was also used, and the loss function used was the Mean Absolute Error (MAE). The GNN was trained over 300 epochs, using 1200 simulations of the 2D Ising Model around the criticality, and evaluated in 400 simulations. Therefore, the trained GNN was used on whole brain networks to estimate the brain temperature over neurodevelopment. The methodology is shown in Fig. 1.

The GNN performance predicting the temperature on the test set was MAE = 0.08 and r2 = 0.70. For the whole brain graphs, age and temperature for healthy subjects were negatively correlated (r = -0.32, two-sided p<0.001). Subjects with ADHD were negatively correlated (r = -0.34, two-sided p<0.001). Moreover, to evaluate the influence of head motion on the Ising Temperate estimation, a linear regression was used. The only variable significant to explain the age was temperature, and it's also negatively associated (coef = -0.92(0.08), two-sided p<0.001).

In this work, functional connectivity and Graph Neural Networks were used to estimate the Ising Temperature of the brain, in order to investigate neurodevelopment. The main finding indicates a statistically significant negative correlation between age and temperature, suggesting that the brain gets distant from criticality as age increases. Moreover, this novel methodology allows more works to investigate the brain network from GNNs trained on simulated dynamical models.

Early life, Adolescence, Aging ¹

Classification and Predictive Modeling

Connectivity (eg. functional, effective, structural)

fMRI Connectivity and Network Modeling ²

Multivariate Approaches

Attention Deficit Disorder

Computational Neuroscience

Data analysis

Development

FUNCTIONAL MRI

Machine Learning

Modeling

Multivariate

Open-Source Code

Other - Connectivity