Reverse engineering the brain input: Network control theory to identify cognitive task-related control nodes

TL;DR

This work addresses the lack of explicit identification of brain inputs during cognitive tasks by casting the brain as a linear dynamical system and formulating a joint optimization to recover both the sparse set of control nodes and their input sequences. Using $x(t+1)=A x(t)+B u(t)$, with $A$ derived from structural connectivity and $B$ encoding selected nodes, the authors solve a relaxed, regularized objective via an augmented Lagrangian method and backpropagation through time. They validate the framework on synthetic data and apply it to motor-task fMRI from 200 HCP subjects, achieving an explained variance around high levels and identifying 28 control nodes that largely align with motor regions. This approach provides a general, control-theoretic tool for understanding brain inputs and their transmission across networks, with potential implications for neuromodulation and clinical interventions. The key contribution is a practical algorithm that jointly infers network controllability structure and temporal inputs from whole-brain imaging data, bridging network control theory and neuroimaging.

Abstract

The human brain receives complex inputs when performing cognitive tasks, which range from external inputs via the senses to internal inputs from other brain regions. However, the explicit inputs to the brain during a cognitive task remain unclear. Here, we present an input identification framework for reverse engineering the control nodes and the corresponding inputs to the brain. The framework is verified with synthetic data generated by a predefined linear system, indicating it can robustly reconstruct data and recover the inputs. Then we apply the framework to the real motor-task fMRI data from 200 human subjects. Our results show that the model with sparse inputs can reconstruct neural dynamics in motor tasks ($EV=0.779$) and the identified 28 control nodes largely overlap with the motor system. Underpinned by network control theory, our framework offers a general tool for understanding brain inputs.

Figures (3)

• Figure 1: Inferring control nodes and input signals. The brain network system is modeled with a linear dynamic model, $\mathbf{x}(t+1)=\mathbf{A}\mathbf{x}(t)+\mathbf{B}\mathbf{u}(t)$. The goal is to identify the control node $B$ and the input sequence $\mathbf{u}(t)$ given the observed fMRI dynamics $\mathbf{x}(t)$ and the pre-defined $\mathbf{A}$.
• Figure 2: Simulating data and reverse engineering inputs. a The generated dynamics by a linear model. b Solution of the reverse problem, including the inferred control nodes (left), their corresponding inputs (middle) and the reconstructed dynamics (right). c The explained variance (EV) between the reconstructed and generated dynamics (left), between the inferred and ground-truth inputs on clean data (middle) and noisy data (right), respectively. The higher the EV, the better the performance.
• Figure 3: Motor task fMRI data and reverse engineering inputs. a Quantification analysis on tuning hyperparameters (the best hyperparameters set: $\lambda_1=0.0001,\lambda_2=0.1 \text{ and } \alpha=28$). b The visualization of the inferred control nodes. c The average activation map of the motor task in the HCP dataset. d Input series of ROIs in the identified control nodes.