Network control theory (NCT) for neuroscientists: a Python-based protocol.
Poster No:
1492
Submission Type:
Abstract Submission
Authors:
Linden Parkes1, Jason Kim2, Julia Brynildsen3, Matthew Cieslak3, Sydney Covitz4, Raquel Gur3, Ruben Gur3, Fabio Pasqualetti5, Russell Shinohara3, Jennifer Stiso3, Dale Zhou5, Theodore Satterthwaite3, Dani Bassett3
Institutions:
1Rutgers University, Philadelphia, PA, 2Cornell University, Ithaca, NY, 3UPenn, Philadelphia, PA, 4Stanford, Palo Alto, CA, 5University of California, Riverside, CA
First Author:
Co-Author(s):
Introduction:
Network neuroscience is principally concerned with studying the connectome, the complete description of the brain's connectivity. This connectome is encoded as a graph of nodes interconnected by edges that can be defined across multiple scales, species, and modalities (1). The connectome gives rise to complex topology, including hubs, modules, small-worldness, and core-periphery structure (2). Understanding how this topology shapes and constrains the brain's rich repertoire of dynamics is a central goal of network neuroscience.
Network control theory (NCT) provides an approach to studying these neural dynamics that yields insights into how they emerge from the topology of the underlying structural connectome. Here, NCT assumes that inter-nodal communication follows a linear model of diffusion, where activity from one set of nodes spreads across the network over time along a series of fronts (2). Then, upon this dynamical system, NCT models a set of external control signals that are designed to guide these diffusing activity patterns towards a chosen target state (i.e., a user-defined pattern of neural activity). These control signals are found by minimizing the total magnitude of their input over a given time horizon; that is, they are designed to achieve a state transition with the lowest amount of control energy. Once modeled, these control signals can be examined to determine to what extent, and how, they were constrained by topology, thus allowing researchers to study how the connectome can be leveraged to control dynamics. To facilitate the application of NCT to neuroscience research, we developed a protocol accompanied by a Python-based software package called nctpy (https://github.com/BassettLab/nctpy).
Network control theory (NCT) provides an approach to studying these neural dynamics that yields insights into how they emerge from the topology of the underlying structural connectome. Here, NCT assumes that inter-nodal communication follows a linear model of diffusion, where activity from one set of nodes spreads across the network over time along a series of fronts (2). Then, upon this dynamical system, NCT models a set of external control signals that are designed to guide these diffusing activity patterns towards a chosen target state (i.e., a user-defined pattern of neural activity). These control signals are found by minimizing the total magnitude of their input over a given time horizon; that is, they are designed to achieve a state transition with the lowest amount of control energy. Once modeled, these control signals can be examined to determine to what extent, and how, they were constrained by topology, thus allowing researchers to study how the connectome can be leveraged to control dynamics. To facilitate the application of NCT to neuroscience research, we developed a protocol accompanied by a Python-based software package called nctpy (https://github.com/BassettLab/nctpy).
Methods:
Our protocol (Fig. 1) guides researchers through the process of modeling dynamics on a structural connectome, defining a state transition, computing the control signals and the associated state trajectory (i.e., simulated neural activity), as well as integrating control signals to compute control energy. We also include tools for deploying null network models, which enable researchers to examine which topological features affect their model outputs.
We tested our protocol on an undirected connectome representing interregional structural connectivity in the group-averaged (n=253) human brain (3). Using nctpy, we computed the control signals required to transition the brain between two activity states; one characterized by activity concentrated in the visual cortex (vis; Fig. 2A, left), and the other characterized by activity in the default mode network (DMN; Fig. 2A, right). These states were extracted from clustering of resting-state fMRI timeseries (4). Next, we integrated these control signals over time, and summed those outputs over brain regions, to obtain control energy. We computed control energy for the vis-to-DMN transition as well as the reverse DMN-to-vis transition.
We tested our protocol on an undirected connectome representing interregional structural connectivity in the group-averaged (n=253) human brain (3). Using nctpy, we computed the control signals required to transition the brain between two activity states; one characterized by activity concentrated in the visual cortex (vis; Fig. 2A, left), and the other characterized by activity in the default mode network (DMN; Fig. 2A, right). These states were extracted from clustering of resting-state fMRI timeseries (4). Next, we integrated these control signals over time, and summed those outputs over brain regions, to obtain control energy. We computed control energy for the vis-to-DMN transition as well as the reverse DMN-to-vis transition.
Results:
We found that control energy was 24% higher for the vis-to-DMN transition (energy=2676) compared to the DMN-to-vis transition (energy=2154), suggesting that the latter transition was easier to complete. Next, we tested these energies against a null network model that preserved both the spatial embedding and the strength sequence of the nodes (5). We found that energy for both the vis-to-DMN (Fig. 2D) and the DMN-to-vis (Fig. 2E) transitions were lower than expected relative to their respective nulls, indicating that the energy associated with these transitions was not explained by a combination of spatial embedding and nodes' strength. This result suggests that these transitions were supported by higher-order topology.
Conclusions:
nctpy provides intuitive tools for performing NCT analysis on connectomes. Users can define their own state transitions, interrogate the corresponding control signals, summarize those signals into control energy, and examine to what extent their results are explained by different aspects of topology.
Modeling and Analysis Methods:
Connectivity (eg. functional, effective, structural) 1
Diffusion MRI Modeling and Analysis 2
Keywords:
Computational Neuroscience
Other - Network control; dynamics; connectivity; communicability;
1|2Indicates the priority used for review
Provide references using author date format
2. Fornito A, Zalesky A, Bullmore ET (2016): Fundamentals of Brain Network Analysis. Elsevier/Academic Press.
3. Satterthwaite TD, Elliott MA, Ruparel K, Loughead J, Prabhakaran K, Calkins ME, et al. (2014): Neuroimaging of the Philadelphia Neurodevelopmental Cohort. NeuroImage 86: 544–553.
4. Cornblath EJ, Ashourvan A, Kim JZ, Betzel RF, Ciric R, Adebimpe A, et al. (2020): Temporal sequences of brain activity at rest are constrained by white matter structure and modulated by cognitive demands. Commun Biol 3: 261.
5. Roberts JA, Perry A, Lord AR, Roberts G, Mitchell PB, Smith RE, et al. (2016): The contribution of geometry to the human connectome. NeuroImage 124: 379–393.