  Electrical conduction among cardiac tissue is commonly modeled with partial
differential equations, i.e., reaction-diffusion equation, where the reaction
term describes cellular stimulation and diffusion term describes electrical
propagation. Detecting and identifying of cardiac cells that produce abnormal
electrical impulses in such nonlinear dynamic systems are important for
efficient treatment and planning. To model the nonlinear dynamics, simulation
has been widely used in both cardiac research and clinical study to investigate
cardiac disease mechanisms and develop new treatment designs. However, existing
cardiac models have a great level of complexity, and the simulation is often
time-consuming. We propose a deep spatio-temporal sparse decomposition (DSTSD)
approach to bypass the time-consuming cardiac partial differential equations
with the deep spatio-temporal model and detect the time and location of the
anomaly (i.e., malfunctioning cardiac cells). This approach is validated from
the data set generated from the Courtemanche-Ramirez-Nattel (CRN) model, which
is widely used to model the propagation of the transmembrane potential across
the cross neuron membrane. The proposed DSTSD achieved the best accuracy in
terms of spatio-temporal mean trend prediction and anomaly detection.
