On Optimal Defibrillating Pulse Synthesis

This article proposes a control framework suitable to study the synthesis of electrical signals that bring a fibrillating heart to a nominal (defibrillated) state so that regular, autonomous cardiac activity resumes. A parallel resistor/capacitor (single RC-circuit) and energy source has been used for over 70 years to describe the heart's defibrillated state as a condition of reaching nominal threshold potential values represented by the capacitor voltage. The bidomain model adopted in the 1990' s was an improvement as it provided 2D and 3D continuum models of cardiac tissue enabling significant advances in modeling electrical cardiac activity. We have spatially discretized a version of the bidomain equations so that the temporal behavior of the transmembrane potential at a point is deduced from an infinite number of first-order differential equations. The connection to a network of RCcircuits is logical and creates opportunities for theoretical and practical modeling and control contributions. A strategy that minimizes a weighted time/energy cost for the single RC-circuit was applied to a multi-RC model. The proposed pulse is agile and energy conscientious thus outperforming the pulse developed to minimize energy consumption alone. The results can also be used to formalize ad-hoc reports that explore the time-energy tradeoff in other defibrillating pulse candidates. In addition, the multi-RC circuit may be used to explore cardiac tissue recovery and multi-path defibrillation. A minimum-time strategy is proposed for the multi-RC circuit to address fast capacitor discharge requirements. These efforts suggest new waveforms to potentially innovate defibrillator design using feedback control.