Dynamic graph vector autoregression for characterizing cardiac electromechanical dynamics during incremental exercise from the joint phase space of electrocardiogram and phonocardiogram

Abnormal cardiac electromechanical coupling (cEMC) is associated with exercise-induced arrhythmias, yet monitoring cEMC during unrestricted movement remains challenging. While electrocardiogram (ECG) and phonocardiogram (PCG) recordings provide indirect measures of cardiac electrical and mechanical activity, each represents only a one-dimensional scalar observation of the cardiac system, and the system’s latent state-space dynamics response to exercise intensity remains inaccessible. Therefore, this study employs Takens’ delayed embedding phase-space reconstruction method to reconstruct the latent state trajectories and then combines them into a joint ECG-PCG phase space. Building on this representation, this study proposes dynamic graph vector autoregression (DG-VAR), a data-driven analytical approach for characterizing latent cEMC from the joint phase space of ECG and PCG during exercise. Benchmarking with an open-access database demonstrated that DG-VAR achieved the highest performance in predicting the joint phase space of ECG and PCG during exercise. The method yielded an average root mean square error (RMSE) of 0.0186 and mean absolute percentage error (MAPE) of 7.76 for ECG phase space predictions, and an average RMSE of 0.0085 and MAPE of 4.45 for PCG phase space predictions. Furthermore, matrix-derived parameters, including stationarity, coupling strength, and dynamic graph topology, showed significant correlations with cardiac electromechanical intervals. Analysis of these parameters revealed an intensity-dependent regulatory pattern in cardiac electromechanical dynamics: forward electromechanical coupling increases monotonically, the feedback mechanism rises initially and then stabilizes, and the network dynamics topology evolves towards a state of greater density and smoothness. This non-invasive, label-free, data-driven analytical framework offers a novel, physiologically interpretable approach to dynamic monitoring of exercise-induced cEMC responses.