Fast interactive simulations of cardiac electrical activity in anatomically accurate heart structures by compressing sparse uniform cartesian grids

Abstract

Background and Objective:

Numerical simulations are valuable tools for studying cardiac arrhythmias. Not only do they complement experimental studies, but there is also an increasing expectation for their use in clinical applications to guide patient-specific procedures. However, numerical studies that solve the reaction–diffusion equations describing cardiac electrical activity remain challenging to set up, are time-consuming, and in many cases, are prohibitively computationally expensive for long studies. The computational cost of cardiac simulations of complex models on anatomically accurate structures necessitates parallel computing. Graphics processing units (GPUs), which have thousands of cores, have been introduced as a viable technology for carrying out fast cardiac simulations, sometimes including real-time interactivity. Our main objective is to increase the performance and accuracy of such GPU implementations while conserving computational resources.

Methods:

In this work, we present a compression algorithm that can be used to conserve GPU memory and improve efficiency by managing the sparsity that is inherent in using Cartesian grids to represent cardiac structures directly obtained from high-resolution MRI and mCT scans. Furthermore, we present a discretization scheme that includes the cross-diagonal terms in the computational cell to increase numerical accuracy, which is especially important for simulating thin tissue sections without the need for costly mesh refinement.

Results:

Interactive WebGL simulations of atrial/ventricular structures (on PCs, laptops, tablets, and phones) demonstrate the algorithm’s ability to reduce memory demand by an order of magnitude and achieve calculations up to 20x faster. We further showcase its superiority in slender tissues and validate results against experiments performed in live explanted human hearts.

Conclusions:

In this work, we present a compression algorithm that accelerates electrical activity simulations on realistic anatomies by an order of magnitude (up to 20x), thereby allowing the use of finer grid resolutions while conserving GPU memory. Additionally, improved accuracy is achieved through cross-diagonal terms, which are essential for thin tissues, often found in heart structures such as pectinate muscles and trabeculae, as well as Purkinje fibers. Our method enables interactive simulations with even interactive domain boundary manipulation (unlike finite element/volume methods). Finally, agreement with experiments and ease of mesh import into WebGL paves the way for virtual cohorts and digital twins, aiding arrhythmia analysis and personalized therapies.