Sliding Mode Control of Cardiac Rhythms in the Sinoatrial Node using Gaussian Process Regression
The Sinoatrial node (SA), also called natural pacemaker, is responsible to initiate the heart electrical activity, usually represented by electrocardiograms (ECGs). Abnormalities at the SA node can produce disordered heart rhythms or, in other words, cardiac arrhythmia that are visualized in the ECGs. The development of control strategies to stabilize the cardiac rhythm at the natural pacemaker can provide efficient ways to deal with and avoid some heart pathology. This paper investigates the use of a robust controller based on sliding modes for cardiac rhythms at the SA node in order to induce normal rhythms from pathological responses. Embedded into this controller, a Gaussian process regressor is utilized to predict and compensate modeling uncertainties and disturbances. A mathematical model that presents close agreement with experimental measurements is employed to represent the heart functioning. The adopted model comprises a network of oscillators formed by sinoatrial node, atrioventricular node (AV) and His-Purkinje complex (HP). Three nonlinear oscillators are employed to represent each one of the nodes that are connected by delayed couplings. The boudedness and convergence properties are investigated with a Lyapunov-like stability analysis. In order to evaluate the ability of the control law to deal with interpatient variability, the heart model is assumed to be not available to the controller designer, being used only in the simulator to assess the control performance. The results show that, by applying the proposed control scheme, abnormal rhythms can be avoided, turning the ECG closer to the expected normal behavior and preventing critical cardiac responses.