Graph-based homogenisation for modelling cardiac fibrosis.

Area of Science:

• Computational biology
• Cardiac electrophysiology
• Numerical methods

Background:

• Fibrosis, characterized by excess extracellular matrix, impairs cardiac action potential propagation.
• The impact of fibrosis on heart function is highly dependent on its location and associated scar formation.
• Computational simulations are crucial for understanding fibrosis effects but are limited by spatial resolution due to computational cost.

Purpose of the Study:

• To develop a novel numerical homogenization technique for simulating cardiac electrophysiology in fibrotic tissue.
• To incorporate fine-scale conductivity heterogeneities into coarser computational meshes efficiently.
• To enable accurate modeling of action potential propagation in complex fibrotic cardiac tissue.

Main Methods:

• A novel numerical homogenization technique combining Eikonal and graph approaches.
• Derivation of effective conductivity tensors to represent fine-scale heterogeneities on a coarser mesh.
• Application of the technique to simulate action potential propagation in 2D fibrotic cardiac tissue models.

Main Results:

• The graph-based homogenization technique accurately captures fine-scale domain information on coarser meshes.
• Demonstrated effectiveness in simulating sharp-fronted traveling waves of activation.
• Successfully modeled excitation propagation in diffuse fibrosis, tunnel-like structures, scar regions, and functional re-entry.

Conclusions:

• The proposed graph-based homogenization technique is accurate and effective for simulating cardiac action potential propagation in fibrotic tissue.
• This method overcomes computational cost limitations, allowing for finer detail in cardiac simulation models.
• The technique offers a valuable tool for understanding the complex effects of fibrosis on heart function.