A Connectome Generative Model with Dynamic Axon Growth
Poster No:
1489
Submission Type:
Abstract Submission
Authors:
Yuanzhe Liu1, Caio Seguin2, Richard Betzel3, Danyal Akarca4, Maria Di Biase1, Andrew Zalesky1
Institutions:
1The University of Melbourne, Melbourne, Victoria, 2Department of Psychological and Brain Sciences, Indiana University, Bloomington, IN, 3Indiana University, Bloomington, IN, 4University of Cambridge, Cambridge, England
First Author:
Co-Author(s):
Introduction:
Connectome generative models provide insight into the wiring mechanisms underpinning connectome topology [1,2]. However, current generative models do not account for the dynamics of axonal growth, limiting their biological interpretability. The aims of this study are threefold: i) to build a connectome generative model that incorporates dynamic axon growth, ii) to develop a method that optimizes model parameters for individual connectomes, and iii) to test if the model can generate brain-like networks and white matter fiber bundles.
Methods:
The cerebral volume is modelled as a 2D circle, with the circumference and the internal space representing brain gray and white matter, respectively. The circumference is randomly parcellated to represent the 84 regions in Desikan-Killiany atlas, otherwise known as nodes (Fig. 1a).
Simulated axons are uniformly seeded at random along the circumference. Each axon propagates step-by-step within the circle, and the direction of propagation is dynamically updated based on a combined attractive force exerted by each node (Fig. 1a-1b). The attractive forces represent axon guiding cues that decay as a function of distance between the node exerting the force and the axon's growth tip. An axon terminates when its tip encounters the circle circumference, forming a connection between its origin and intersection with the circle (Fig. 1c). Generated networks are constructed by counting the number of axons interconnecting each pair of nodes (Fig. 1d-1e).
Two key model parameters control network topology: The force decay parameter β, and the axon growth length of each extending step L. Using an extensive grid search, we first examined how generated network topology, in terms of small-worldness and modularity, varied with respect to parameters. Next, we mapped structural connectomes for 1064 participants of the Human Connectome Project (HCP) and fitted model parameters to individual connectomes by minimizing the difference in above-mentioned topological measures, between empirical and generated networks. Finally, we generated networks with fitted parameters and tested if the generated networks recapitulate connectomic properties that the parameters were not optimized for.
Simulated axons are uniformly seeded at random along the circumference. Each axon propagates step-by-step within the circle, and the direction of propagation is dynamically updated based on a combined attractive force exerted by each node (Fig. 1a-1b). The attractive forces represent axon guiding cues that decay as a function of distance between the node exerting the force and the axon's growth tip. An axon terminates when its tip encounters the circle circumference, forming a connection between its origin and intersection with the circle (Fig. 1c). Generated networks are constructed by counting the number of axons interconnecting each pair of nodes (Fig. 1d-1e).
Two key model parameters control network topology: The force decay parameter β, and the axon growth length of each extending step L. Using an extensive grid search, we first examined how generated network topology, in terms of small-worldness and modularity, varied with respect to parameters. Next, we mapped structural connectomes for 1064 participants of the Human Connectome Project (HCP) and fitted model parameters to individual connectomes by minimizing the difference in above-mentioned topological measures, between empirical and generated networks. Finally, we generated networks with fitted parameters and tested if the generated networks recapitulate connectomic properties that the parameters were not optimized for.
Results:
Within the parameter space evaluated, generated networks were consistently characterized by a small-world and modular organization. Despite this, variations in model parameters altered the strengths of small-worldness and modularity in a continuous manner, such that increasing β and/or decreasing L resulted in stronger clustering and small-worldness, longer characteristic path length, and weaker modularity. By minimizing the small-world and modular disparity between empirical and generated networks, we optimized model parameters of connectomes mapped for HCP participants (Fig. 2a).
The networks generated with our model not only displayed brain-like small-worldness and modularity, but also recapitulated several properties characterizing empirical connectomes that the parameters were not optimized for (Fig. 2b). Specifically, generated networks showed realistic axonal fascicle structures (i.e. short-range U-fibers and long-range bundles), negatively correlated connection weight and distance [5,7], strong long-range connections that deviated from the exponential distance rule [6], lognormally distributed connection weights [5], and scale-free degree distributions [3,4].
The networks generated with our model not only displayed brain-like small-worldness and modularity, but also recapitulated several properties characterizing empirical connectomes that the parameters were not optimized for (Fig. 2b). Specifically, generated networks showed realistic axonal fascicle structures (i.e. short-range U-fibers and long-range bundles), negatively correlated connection weight and distance [5,7], strong long-range connections that deviated from the exponential distance rule [6], lognormally distributed connection weights [5], and scale-free degree distributions [3,4].
Conclusions:
The present study developed a connectome generative model that features dynamic axon outgrowth. The model recapitulated a diverse array of topological features characteristic of nervous systems, at the connection, node, and network levels. A parameter inference approach was proposed, enabling parameter optimization for individual connectomes. Overall, our work enables generation of connectomes in silico that are weighted, spatially embedded, and feature axonal trajectories that appear biologically realistic.
Modeling and Analysis Methods:
Connectivity (eg. functional, effective, structural) 1
Diffusion MRI Modeling and Analysis
Other Methods
Neuroanatomy, Physiology, Metabolism and Neurotransmission:
White Matter Anatomy, Fiber Pathways and Connectivity 2
Keywords:
Computational Neuroscience
MRI
1|2Indicates the priority used for review
Provide references using author date format
[2] Betzel, R. F. (2016). "Generative models of the human connectome." Neuroimage 124: 1054-1064.
[3] Broido, A. D. (2019). "Scale-free networks are rare." Nature communications 10(1): 1017.
[4] Clauset, A. (2009). "Power-law distributions in empirical data." SIAM review 51(4): 661-703.
[5] Ercsey-Ravasz, M. (2013). "A predictive network model of cerebral cortical connectivity based on a distance rule." Neuron 80(1): 184-197.
[6] Roberts, J. A. (2016). "The contribution of geometry to the human connectome." Neuroimage 124: 379-393.
[7] Song, H. F. (2014). "Spatial embedding of structural similarity in the cerebral cortex." Proceedings of the National Academy of Sciences 111(46): 16580-16585.