The EMI (Extra, Intra, Membrane) model, also known as the cell-by-cell model, is a numerical building block in computational electrophysiology, typically used, at a cellular scale, to simulate excitable tissues. For example, in homogenized models, such as the mono and bidomain equations, the EMI model resolves cells morphologies, enabling detailed biological simulations. For example, inhomogeneities in ionic channels along the membrane, as observed in myelinated neuronal axons, can be described within the EMI model. EMI models have many applications for example in computational cardiology and neuroscience, where spreading excitation by electrical signalling plays a crucial role.
In the interesting paper under review, the authors are interested in solving large linear systems stemming from the EMI. After setting the related systems of partial differential equations equipped with proper boundary conditions, the authors provide their finite element discretizations and focus on the resulting large linear systems. They provide a relatively complete spectral analysis using tools from the theory of Generalized Locally Toeplitz matrix sequences. The spectral information obtained is then used for designing appropriate preconditioned Krylov solvers. Through numerical experiments, the authors illustrate that the presented solution strategy is robust with respect to problem and discretization parameters, efficient and scalable.
The paper is well written with a good set of references.