Automatic construction of interconnected cable models of cardiac propagation on a surface

Cardiac fibers may be represented by a network of interconnected cables for simulating electrical propagation. The lack of automatic cable mesh generation tool has hampered this modeling approach. We aim to provide and evaluate an algorithmic solution to this problem.

We developed an open-source C++/Python package for the construction of a monolayer interconnected cable model from a triangulated surface with fiber orientation, targeting a given longitudinal and transverse space step. The workflow of the algorithm starts with the generation of evenly spaced streamlines aligned with fiber orientation. Another set of streamlines, orthogonal to the fibers, is used to specify lateral connections. The intersection between the two sets of streamlines gives the vertices of the cable mesh, determines its connectivity, and defines a polygonal tessellation of the surface that can be triangulated. Finite differences can then be applied to solve a reaction-diffusion equation on the cable mesh.

The approach was validated in increasingly complex configurations and up to near-cellular resolutions (20 to 200μm). Fiber orientation noise, singularities and abrupt changes in orientation reduced the local coupling by altering the microstructure of the tissue. The pipeline for mesh generation was tested using a publicly available cohort of 98 patient-specific geometries. The stability limit of the numerical scheme was assessed by spectral analysis of the diffusion matrix and was compared to triangular meshes and cartesian grids.

This physiologically based mesh generation tool may be used as a building block for the construction of multilayer three-dimensional models of the atria for the simulation of discrete propagation.