(448f) Cardiac Alternans Annihilation By Optimal and Model Predictive Control

Cardiac alternans are defined as the beat-to-beat oscillations of the action potential duration (APD) in paced cardiac cells. This phenomena has been identified as a possible precursor to ventricular arrhythmia and even sudden cardiac death. The annihilation of these alternans is therefore a promising anti-arrhythmic strategy that requires more exploration within the realm of cardiac implantable devices.

In this work, optimal and model predictive controllers are implemented on the small amplitude of alternans parabolic partial differential equation (PDE). This PDE was developed by [1], and describes the dynamics of the amplitude of alternans along a cable of cardiac cells with a finite length. In our proposed control strategy, both electrical and mechanical stimuli are utilized to annihilate the alternans along the length of the cable. The electrical stimulus represents a pacer which is applied at the cable’s boundary, while the mechanical stimuli are spatially distributed along the cable and affect the APD by altering the intracellular calcium dynamics.

In previous work, it has been demonstrated that the successful annihilation of cardiac alternans can be achieved using a low dimensional optimal controller [2]. However, optimal controllers might violate the system’s naturally present physiological constraints. This provides the motivation to develop a model predictive controller for the cardiac system in which the constraints are explicitly accounted for. We demonstrate that by using the MPC formulation of [3], stabilization of the alternans along the cable is achieved. Furthermore, satisfaction of the input constraints arising from the actuator limitations (pacing limitations) as well as state constraints which are naturally present in the cardiac system is also achieved through this MPC formulation.

Finally, we address the issue of uncertainties in the PDE parameters by studying the robust stability of the closed loop system. These uncertainties arise from the fact that the PDE parameters are obtained by applying a pacing algorithm on a single cell ionic model, and therefore will vary depending on the choice of ionic model.

References

[1] B. Echebarria and A. Karma Instability and spatiotemporal dynamics of alternans in paced cardiac tissue. Physical Review Letters, vol. 88 (2002), no. 20, pp. 208101.1-208101.

[2]  S. Dubljevic and P.D. Christofides Optimal mechano-electric stabilization of cardiac alternans. Chemical Engineering Science, vol. 63 (2008), pp. 5425-5433

[3]  K.R. Muske and J.B. Rawlings Linear model predictive control of unstable processes. J. Proc. Cont., vol. 3 (1993), no. 2, pp. 85 - 96