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Simulation of Robustness against Lesions of Cortical Networks
Marcus Kaiser, Robert Martin, Peter Andras, Malcolm P. Young
TL;DR
The paper investigates whether cortical connectivity resembles scale-free networks and whether structural connectivity can characterize robustness to brain lesions. It compares cat and macaque cortical networks with benchmark networks using node and connection removals and ASP analysis. Cortical structural decay is largely similar to scale-free networks, implicating hubs and bottleneck connections in conditional robustness.
Problem
The study addresses whether cortical structural connectivity has scale-free properties and whether connectivity data can evaluate variable robustness and lesion effects.
Method
The authors compare cat and macaque cortical inter-area networks with random, scale-free, small-world, and rewired benchmarks using graph similarity and ASP changes after node or connection removal.
Results
Cortical networks’ structural decay is largely similar to scale-free networks, including responses to elimination of nodes and connections.
Takeaways & Limitations
Highly connected hubs and bottleneck connections appear to form structural bases for some conditional robustness of brain systems.
Takeaways & Limitations
Direct comparison of cortical degree distributions was impossible, and the analysis excluded interhemispheric and subcortical connections.
Abstract
from arXiv · showhide
Structure entails function and thus a structural description of the brain will help to understand its function and may provide insights into many properties of brain systems, from their robustness and recovery from damage, to their dynamics and even their evolution. Advances in the analysis of complex networks provide useful new approaches to understanding structural and functional properties of brain networks. Structural properties of networks recently described allow their characterization as small-world, random (exponential) and scale-free. They complement the set of other properties that have been explored in the context of brain connectivity, such as topology, hodology, clustering, and hierarchical organization. Here we apply new network analysis methods to cortical inter-areal connectivity networks for the cat and macaque brains. We compare these corticocortical fibre networks to benchmark rewired, small-world, scale-free and random networks, using two analysis strategies, in which we measure the effects of the removal of nodes and connections on the structural properties of the cortical networks. The brain networks' structural decay is in most respects similar to that of scale-free networks. The results implicate highly connected hub-nodes and bottleneck connections as structural basis for some of the conditional robustness of brain systems. This informs the understanding of the development of brain networks' connectivity.
INTRODUCTION
The study asks whether cortical connectivity networks resemble scale-free networks and whether their robustness to simulated damage can be evaluated from connectivity structure. Using cat and macaque cortical networks, it compares structural similarity and ASP changes after targeted or random removal of nodes and connections with benchmark networks.
- The brain’s contradictory responses to lesions motivate evaluating effective robustness and predicting the severity and nature of localized damage from connectivity data.
- Scale-free networks are robust to randomly located damage but sensitive to targeted damage at highly connected nodes, paralleling reported properties of the brain.
- Cortical networks from cat and macaque show highly connected and sparsely connected areas relative to random networks, resembling scale-free degree distributions.
- Direct degree-distribution power-law testing is unsuitable because cortical networks have low maximum degrees, few nodes, and incomplete connectivity sampling; indirect measures are therefore used.
- Degree-ordered graph similarity is higher between cortical and scale-free networks than between cortical and random or small-world networks.
- Targeted removal of highly connected nodes produces a sharp ASP rise and fragmentation in brain networks, with cat responses largely within the 95% confidence interval of scale-free benchmarks.
- Scale-free benchmarks are the only networks with similar maximal ASP and peak-deletion fractions for both cat and macaque cortical networks.
- The analysis compares cortical inter-area networks with random, scale-free, small-world, and rewired benchmarks using node- and connection-removal effects on ASP.
Tables
The tables compare cortical brain networks with matched benchmark networks using path-length and clustering statistics, and summarize the most highly connected regions.
- Table 1: Table 1 reports average shortest path and clustering coefficient statistics for macaque and cat cortical networks and matched benchmark networks.Benchmark values are given as means and standard deviations across 50 generated networks.
- Table 2: Table 2 lists the highest-degree cat and macaque regions together with their incoming and outgoing connection counts.The table gives degree, in-degree, and out-degree, with maximum possible totals of 110 connections for cat and 130 for macaque.
Figures
The figures compare network topology, degree distributions, connectivity similarity, and structural decay under targeted or random removals. Across these views, cortical networks are compared with random, small-world, rewired, and scale-free benchmarks.
- Figure 1: Figure 1 contrasts a scale-free network containing highly connected hubs with a random network having the same numbers of nodes and edges.The hub is shown centrally in the scale-free schematic.
- Figure 2: Figure 2 compares macaque and cat degree-distribution histograms with binomial random-network distributions using p=0.1417 and p=0.2643, respectively.Gray histograms represent cortical networks, while black distributions represent random networks.
- Figure 3: Figure 3 compares cortical-network edge similarity with 1,000 generated rewired, scale-free, small-world, and random benchmark networks.Scale-free similarity matches rewired cortical networks, whereas random and small-world similarity is significantly lower.
- Figures 4–5: Figures 4 and 5 plot average shortest path against the fraction of deleted nodes for targeted and random removals in macaque and cat networks and their benchmarks.Targeted removal follows connectivity order; random removal uses a random node order.
- Figure 6: Figure 6 summarizes the fraction of targeted node removals producing peak average shortest path and the corresponding peak value across benchmark networks.Means and standard deviations are shown for 50 generated benchmark networks; scale-free peak-removal fractions are closest to cortical values.
- Figure 7: Figure 7 summarizes the fraction and value of peak average shortest path during targeted connection elimination across cortical and benchmark networks.The cat network has scale-free and small-world peak fractions similar to its cortical value, while rewired and random fractions are higher.