fscpy 1.0.1

Function to Structure Coupling (FSC)

FSC (Function–Structure Coupling)

FSC is a Python implementation of the Function–Structure Coupling model, an edge-centric framework for analyzing brain connectivity using constrained Laplacians.

The method links functional connectivity (FC) and structural connectivity (SC) by solving a network flow model that explains functional interactions through structural pathways.

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Installation

Install FSC from PyPI:

pip install fscpy

Import in Python:

from fsc import FSC

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Overview

FSC formulates function-structure coupling as a constrained network problem:

• Functional connectivity (FC) defines pairwise constraints (imposed potential differences)
• Structural connectivity (SC) defines the network topology and weights
• The model solves for nodal potentials (φ) and edge-level currents (I)

Mathematically:

I_ij = SC_ij * (φ_i - φ_j)

where:

• φ = nodal potentials
• SC = structural connectivity (weights)
• I = edge-level current (flow)

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Quick Example

from enigmatoolbox.datasets import load_sc, load_fc
from fsc import FSC

# Load connectivity matrices
fc_ctx, _, _, _ = load_fc()
sc_ctx, _, _, _ = load_sc()

# Run FSC model
fsc = FSC(FC=fc_ctx, SC=sc_ctx)

# Get outputs
phi = fsc.get_nodal_potentials()
edge_currents = fsc.get_edge_currents()

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Outputs

Main methods:

• get_nodal_potentials()
  → Nodal potentials (φ)

• get_edge_currents()
  → Edge-level currents (I)

• get_voltage_difference_matrix()
  → Pairwise potential differences (φ_i − φ_j)

• get_graph_laplacian()
  → Structural graph Laplacian

• get_streamline_currents()
  → Streamline-wise currents (for tractography applications)

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Examples

See the examples/ directory for:

• ENIGMA Toolbox example
• Visualization scripts

Run an example:

python examples/enigma_example.py

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Optional Dependencies

Some examples require additional packages:

pip install enigmatoolbox nilearn

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Notes

• FC is interpreted as imposed pairwise potential differences
• SC is treated as a weighted adjacency matrix (conductance)
• Only the upper triangle of FC is used to define constraints
• The model uses Modified Nodal Analysis (MNA)

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Applications

FSC can be used for:

• Studying function-structure coupling in brain networks
• Identifying structural pathways supporting functional connectivity
• Network flow analysis on connectomes
• Tractography filtering and visualization

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Reference

Sairanen, Viljami.
From nodes to pathways: an edge-centric model of brain function-structure coupling via constrained Laplacians
https://doi.org/10.1101/2024.03.03.583186

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Author

Viljami Sairanen

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License

MIT License (see LICENSE file)