Structural Constraints on Complexity: Scaling of Attractors in the Human Connectome

Poster No:

1247 

Submission Type:

Abstract Submission 

Authors:

Sarah Alizadeh1, Bita Shariatpanahi1, Hamidreza Jamalabadi1

Institutions:

1University of Marburg, Marburg, Hessen

First Author:

Sarah Alizadeh  
University of Marburg
Marburg, Hessen

Co-Author(s):

Bita Shariatpanahi  
University of Marburg
Marburg, Hessen
Hamidreza Jamalabadi  
University of Marburg
Marburg, Hessen

Introduction:

A prominent hypothesis in theoretical neuroscience suggests that the brain's functional complexity arises from a large number of stable attractors within its dynamics. According to frameworks like Maximum Entropy Models (MEM) and spin-glass theories, systems with pairwise interactions among N elements can exhibit an exponential increase in the number of stable attractors as system size increases. This exponential scaling implies that increasing the size of a system dramatically expands its dynamical landscape, creating a vast repertoire of stable states. However, whether this theoretical scaling holds for biological networks, such as the human structural connectome, remains elusive, a question which is the subject of this poster.

Methods:

To address this question, we analyzed diffusion spectrum imaging (DSI) data from 30 healthy adult subjects as described in Betzel et al. (2016). Structural connectivity matrices were generated by counting the number of streamlines connecting pairs of brain regions, normalized by the regions' volumes, resulting in a 129 × 129 connectivity matrix for each subject. We modeled the energy landscape of each structural network using a binary spin-model framework, where each brain region could adopt one of two states: active or inactive. The overall energy of the network was determined by summing up the contributions from all connections between regions, weighted by the structural connectivity.
To identify attractors, we initialized the system in 1,000 random states and iteratively adjusted the state of each region to minimize the overall energy. This process continued until the system reached a stable configuration, or attractor, where no further energy reduction was possible. By systematically increasing the number of brain regions included in the analysis-starting with subsets of 5 regions and incrementally adding 5 more at each step up to the full network size of 129 regions. For each subset size and subject, we recorded the total number of attractors, their basin sizes (the fraction of initial states that lead to a given attractor), and their energy depths (a measure of stability based on the energy difference between an attractor and the nearest higher-energy state). Additionally, we computed transition costs, which reflect the energy required to move between neighboring attractors.

Results:

As we increased the number of included brain regions in the model, we observed that the number of attractors initially increased, reaching a peak at N=45 with a mean of 130.2 ± 55.3 attractors across subjects. Beyond N=60, the number of attractors plateaued and oscillated between 65 and 85, far fewer than the exponential scaling predicted by theoretical models. Transition costs, reflecting the energy required to move between attractors, increased slightly with N, plateauing near N=100. This suggests that as the network expands, the energy landscape becomes more rugged, with attractors becoming more energetically isolated. Meanwhile, mean basin size decreased sharply as N increased, stabilizing around N=25. This indicates that while attractors dominate larger portions of the state space in smaller networks, additional regions fragment the state space across existing attractors without creating fundamentally new stable configurations. Finally, the energy depth of attractors remained stable beyond N=45, showing no systematic changes in intrinsic attractor stability as network size increased.

Conclusions:

These findings demonstrate that structural brain networks support a limited number of attractors, with the growth slowing and plateauing as more regions are added to the network. While the energy landscape becomes increasingly rugged and fragmented-evidenced by higher transition costs and smaller basin sizes-the stability of individual attractors remains unchanged. This structural constraint challenges the idea that functional complexity arises from an exponential expansion of attractors.

Modeling and Analysis Methods:

Connectivity (eg. functional, effective, structural) 1
Diffusion MRI Modeling and Analysis
Multivariate Approaches 2

Neuroanatomy, Physiology, Metabolism and Neurotransmission:

White Matter Anatomy, Fiber Pathways and Connectivity

Novel Imaging Acquisition Methods:

Diffusion MRI

Keywords:

Computational Neuroscience
Data analysis
MRI
Multivariate
Statistical Methods
STRUCTURAL MRI
White Matter

1|2Indicates the priority used for review

Abstract Information

By submitting your proposal, you grant permission for the Organization for Human Brain Mapping (OHBM) to distribute your work in any format, including video, audio print and electronic text through OHBM OnDemand, social media channels, the OHBM website, or other electronic publications and media.

I accept

The Open Science Special Interest Group (OSSIG) is introducing a reproducibility challenge for OHBM 2025. This new initiative aims to enhance the reproducibility of scientific results and foster collaborations between labs. Teams will consist of a “source” party and a “reproducing” party, and will be evaluated on the success of their replication, the openness of the source work, and additional deliverables. Click here for more information. Propose your OHBM abstract(s) as source work for future OHBM meetings by selecting one of the following options:

I do not want to participate in the reproducibility challenge.

Please indicate below if your study was a "resting state" or "task-activation” study.

Other

Healthy subjects only or patients (note that patient studies may also involve healthy subjects):

Healthy subjects

Was this research conducted in the United States?

No

Were any human subjects research approved by the relevant Institutional Review Board or ethics panel? NOTE: Any human subjects studies without IRB approval will be automatically rejected.

Not applicable

Were any animal research approved by the relevant IACUC or other animal research panel? NOTE: Any animal studies without IACUC approval will be automatically rejected.

Not applicable

Please indicate which methods were used in your research:

Structural MRI

For human MRI, what field strength scanner do you use?

3.0T

Which processing packages did you use for your study?

FSL

Provide references using APA citation style.

1. Betzel, R. F., Gu, S., Medaglia, J. D., Pasqualetti, F., & Bassett, D. S. (2016). Optimally controlling the human connectome: The role of network topology. Scientific reports, 6(1), 30770.

UNESCO Institute of Statistics and World Bank Waiver Form

I attest that I currently live, work, or study in a country on the UNESCO Institute of Statistics and World Bank List of Low and Middle Income Countries list provided.

No