Deep learning and whole-brain networks for biomarker discovery: modeling the dynamics of brain fluctuations in resting-state and cognitive tasks

TL;DR

This study tackles biomarker discovery for brain states by inferring bifurcation parameters $a_j$ from a Hopf-based whole-brain network. A deep-learning pipeline is trained on synthetic BOLD signals generated under calibrated network dynamics and then applied to 1{,}003 HCP subjects across resting-state and seven tasks to predict $a_j$. The results show significant separation between task and rest distributions ($p<0.0001$ for most comparisons), higher brain-state bifurcation values during tasks, and an image-based input strategy that improves parameter prediction; individual classifiers achieve meaningful accuracy (~62.7%) using the inferred features, indicating subject-specific information in $a_j$. These findings support a scalable, model-driven framework for brain-state characterization with potential applications in cognitive neuroscience and neurological disorder assessment, while highlighting methodological considerations such as permutation sensitivity and the promise of permutation-invariant architectures.

Abstract

Background: Brain network models offer insights into brain dynamics, but the utility of model-derived bifurcation parameters as biomarkers remains underexplored. Objective: This study evaluates bifurcation parameters from a whole-brain network model as biomarkers for distinguishing brain states associated with resting-state and task-based cognitive conditions. Methods: Synthetic BOLD signals were generated using a supercritical Hopf brain network model to train deep learning models for bifurcation parameter prediction. Inference was performed on Human Connectome Project data, including both resting-state and task-based conditions. Statistical analyses assessed the separability of brain states based on bifurcation parameter distributions. Results: Bifurcation parameter distributions differed significantly across task and resting-state conditions ($p < 0.0001$ for all but one comparison). Task-based brain states exhibited higher bifurcation values compared to rest. Conclusion: Bifurcation parameters effectively differentiate cognitive and resting states, warranting further investigation as biomarkers for brain state characterization and neurological disorder assessment.

Figures (5)

• Figure 1: Overview of the training and inference pipelines for predicting bifurcation parameters from BOLD signals. (A) Synthetic BOLD data is generated using a brain network model based on the supercritical Hopf bifurcation, following a parameter sweep to determine the optimal coupling factor. A deep learning model is trained to predict the bifurcation parameters for each brain node using either a time series or an image-based approach. The converter block, bordered by a dotted line, is used exclusively in the image-based approach. (B) Preprocessed BOLD data from the Human Connectome Project is used to estimate bifurcation parameter values across cohorts. After normalization and windowing, BOLD signals are processed through a trained deep learning model to generate predictions. These predicted values provide insights into the underlying brain states across different tasks and resting conditions. The data dimensionality includes $C=8$ cohorts, $S=1,003$ subjects, $T$ scan time steps, and $W=50$ window time steps. The value of $T$ varies within each scan. Note a key distinction: empirical data is used for selecting the optimal coupling factor and for inference, while synthetic data is used only for model training.
• Figure 2: Determination of optimal coupling factor $G$ and statistical comparison of bifurcation parameters across cohorts. (A) The optimal global coupling factor $G$ was estimated through a parameter sweep, minimizing the Kolmogorov-Smirnov distance between the FCD of empirical and simulated BOLD data. The polynomial fit identifies the $G$ value that best aligns the simulated data with the observed resting-state FCD patterns. (B) Distribution of mean bifurcation parameter values across different cognitive task and resting-state cohorts. Statistical significance between cohorts is assessed using the Mann-Whitney-Wilcoxon test, with Benjamini-Hochberg correction applied to control for multiple comparisons. Statistical significance is indicated by **** for $p<=0.0001$, *** for $0.0001<p<=0.001$, ** for $0.001<p<=0.01$, * for $0.01<p<=0.05$ and "ns" for $0.05<p<=1$. These results reveal distinguishable brain state characteristics associated with each cognitive task.
• Figure 3: Individual-level classification of cohorts using bifurcation parameters. (A) Confusion matrix of the linear SVM classifier on the held-out test set for the 8-class (seven tasks and rest) classification problem. Each cell contains the raw count of predictions. The color intensity is normalized by row, representing the recall for each true class (darker green indicates higher recall). The diagonal highlights successful classification, while off-diagonal elements show specific confusion patterns between states. (B) Permutation feature importance of the top 30 most influential brain regions for the classification. The y-axis shows the mean decrease in model accuracy after permuting the values for each region 10 times. Error bars represent the standard deviation across permutations. Brain regions are colored by their corresponding brain networks as defined by the Yeo atlas (also including subcortical).
• Figure 4: Task-based differences in mean bifurcation parameters across brain networks. The mean bifurcation parameter values were calculated across cortical nodes grouped by brain network using the Yeo atlas for each task. These values were then normalized by subtracting the corresponding mean bifurcation parameter for the resting-state cohort. Each cell represents the average difference per network, with colors indicating the magnitude of the difference. Networks are organized by tiers based on overall activation intensity.
• Figure 5: Examples of BOLD time series converted to images for model input in the image-based approach. Each image represents a single window, with height equal to $N$ (the number of nodes) and width equal to $W$ (the number of time steps chosen). The color scale on the right indicates signal values.