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. 2023 Oct 13;24(1):389.
doi: 10.1186/s12859-023-05513-8.

lifex-ep: a robust and efficient software for cardiac electrophysiology simulations

Pasquale Claudio Africa  1   2 , Roberto Piersanti  3 , Francesco Regazzoni  1 , Michele Bucelli  1 , Matteo Salvador  1   4 , Marco Fedele  1 , Stefano Pagani  1 , Luca Dede'  1 , Alfio Quarteroni  1   5
Affiliations

lifex-ep: a robust and efficient software for cardiac electrophysiology simulations

Pasquale Claudio Africa et al. BMC Bioinformatics. .

Abstract

Background: Simulating the cardiac function requires the numerical solution of multi-physics and multi-scale mathematical models. This underscores the need for streamlined, accurate, and high-performance computational tools. Despite the dedicated endeavors of various research teams, comprehensive and user-friendly software programs for cardiac simulations, capable of accurately replicating both normal and pathological conditions, are still in the process of achieving full maturity within the scientific community.

Results: This work introduces [Formula: see text]-ep, a publicly available software for numerical simulations of the electrophysiology activity of the cardiac muscle, under both normal and pathological conditions. [Formula: see text]-ep employs the monodomain equation to model the heart's electrical activity. It incorporates both phenomenological and second-generation ionic models. These models are discretized using the Finite Element method on tetrahedral or hexahedral meshes. Additionally, [Formula: see text]-ep integrates the generation of myocardial fibers based on Laplace-Dirichlet Rule-Based Methods, previously released in Africa et al., 2023, within [Formula: see text]-fiber. As an alternative, users can also choose to import myofibers from a file. This paper provides a concise overview of the mathematical models and numerical methods underlying [Formula: see text]-ep, along with comprehensive implementation details and instructions for users. [Formula: see text]-ep features exceptional parallel speedup, scaling efficiently when using up to thousands of cores, and its implementation has been verified against an established benchmark problem for computational electrophysiology. We showcase the key features of [Formula: see text]-ep through various idealized and realistic simulations conducted in both normal and pathological scenarios. Furthermore, the software offers a user-friendly and flexible interface, simplifying the setup of simulations using self-documenting parameter files.

Conclusions: [Formula: see text]-ep provides easy access to cardiac electrophysiology simulations for a wide user community. It offers a computational tool that integrates models and accurate methods for simulating cardiac electrophysiology within a high-performance framework, while maintaining a user-friendly interface. [Formula: see text]-ep represents a valuable tool for conducting in silico patient-specific simulations.

Keywords: Cardiac electrophysiology; Computational cardiology; Finite element method; High-performance computing; Mathematical modeling.

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Conflict of interest statement

The authors declare that they have no competing interests.

Figures

Fig. 1
Fig. 1
The lifex library encompasses essential features and a framework for numerically solving Finite Element problems. lifex-ep is a publicly released package designed for cardiac electrophysiology simulations based on lifex. Left picture icons sourced from https://fontawesome.com/license
Fig. 2
Fig. 2
Multiscale cardiac electrophysiology model. From the largest to the smallest spatial scale: a organ; b tissue; c cell; d membrane
Fig. 3
Fig. 3
a Computational domain Ω⊂R3 in an idealized slab of ventricular myocardium, partitioned in three subdomains (Ω¯=Ω¯1∪Ω¯2∪Ω¯3), where Γ12 and Γ23 denote the interfaces among the corresponding subdomains; (b) Representation of the orthonormal triplet for the myofiber orientations f0 (fiber, in red), s0 (sheet, in blu) and n0 (sheet-normal, in green) in an idealized slab of ventricular tissue
Fig. 4
Fig. 4
Domains and meshes used in the numerical examples. Domains in the top row a–c are composed of a single subdomain, while for domains in the middle row d–f, zoomed on the bottom g–i, colors are used to differentiate the subdomains
Fig. 5
Fig. 5
Fiber field computed using Laplace-Dirichlet Rule-Based Methods [15, 17] visualized as streamlines: a Slab tissue; b Idealized left atrium; c Idealized left ventricle; d Ventricular slab; e Realistic left atrium; f Realistic left ventricle. The Laplace solution ϕ is the transmural function where ϕ=0 on the endocardium and ϕ=1 on the epicardium
Fig. 6
Fig. 6
Snapshots of the transmembrane potential for all test cases: a Slab tissue; b Idealized left atrium; c Idealized left ventricle; d Ventricular slab; e Realistic left atrium; f Realistic left ventricle
Fig. 7
Fig. 7
Activation maps computed for all the test cases: a Slab tissue; b Idealized left atrium; c Idealized left ventricle; d Ventricular slab; e Realistic left atrium; f Realistic left ventricle
Fig. 8
Fig. 8
Activation times evaluated along the cuboid diagonal line in the N-version benchmark problem [84] for all the numerical solutions performed with lifex-ep at different refinements in space and time. Red lines=Hexahedral simulations; Blue lines=Tetrahedral simulations
Fig. 9
Fig. 9
a Activation times evaluted along the cuboid diagonal and in the points P1, P9 and P8 in the N-version benchmark problem [84]. b Comparison of the lifex-ep numerical solutions (with Red line=Hexahedral mesh and Blue line=Tetrahedral mesh) with respect to the other codes partecipating to the benchmark problem [84]
Fig. 10
Fig. 10
Computational time (left) and parallel speedup (right) against the number of cores for the strong scalability test. Dashed lines indicate the ideal linear scaling
Fig. 11
Fig. 11
Total memory occupation (left) and memory occupation per core with three differently refined meshes
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