Chaos Control

Controlling chaotic dynamics in excitable media is key for terminating cardiac fibrillation. With each heartbeat, electrical excitation waves propagate across the heart muscle, leading to coordinated mechanical contraction and efficient pumping. During cardiac fibrillation, however, excitation waves are chaotic, resulting in incoherent contraction and loss of mechanical function. In clinics, for lack of a better strategy, high-energy electric shocks are being used to terminate arrhythmia and restore normal function. However, these shocks have severe side effects, including tissue damage, excruciating pain, and a worsening prognosis. There is a significant need for better control of ventricular and atrial arrhythmias. Low-energy control of fibrillation aims to replace the single highenergy shock with a sequence of weak pulses. While simple pacing sequences have shown some remarkable success, further optimization is necessary to achieve clinically relevant energy reduction. In this report, we describe recent progress in the development of adaptive and optimized pacing sequences and discuss numerical and experimental evidence demonstrating the significant potential of feedback pacing.

Adaptive Deceleration Pacing (ADP)
Adaptive deceleration pacing (ADP) is an algorithm for determining a sequence of far-field electrical pulses based on the power spectrum of the arrhythmia [1]. In contrast to previous approaches, which often rely only on the dominant frequency of the broad spectrum of fibrillation, ADP relies on the entire spectrum as illustrated in Fig. 8.13. Starting from a high frequency, ADP gradually slows the electrical far-field pacing rate, decelerating the arrhythmia to termination. Confirmed in ex vivo experiments in isolated rabbit hearts, ADP shows robust and effective termination of ventricular and atrial arrhythmias as shown in Fig. 8.14. Supported by MPG technology transfer funds, we are conducting a preclinical in vivo validation of ADP in a large animal disease model of AF in preparation of a first-in-patient study.

The role of pulse timing in cardiac fibrillation
Success rates of simulated single and multi-pulse defibrillation protocols are sensitive to application timing with individual, protocol-specific optimal timings [3, 4] as illustrated in Fig. 8.15. Simulations of defibrillation attempts showed that such timing matters: The success rate of single- pulse protocols can vary by as much as 80 percentage points or more depending on timing, and using more shocks in succession only lessens this sensitivity up to a point [4]. The optimal application timings are found to be specific to each combination of protocol and fibrillation episode [4]. Therefore, feedback-driven inter-pulse periods may be the only feasible means of leveraging timing for improvements in treatment efficacy.

Optimizing Pulse Sequences using Genetic Algorithm
Using 2D simulations of homogeneous cardiac tissue and a genetic algorithm, we demonstrate the optimization of sequences with nonuniform pulse energies and time intervals between consecutive pulses for efficient VF termination [5]. We further identify model-dependent reductions of total pacing energy ranging from 4% to 80% compared to ADP.

Local Minima Feedback Pacing
In a numerical study, we investigated a variant of feedback pacing, in which electrical field pulses are applied after local minima in the mean value of the transmembrane potential [2]. We show that local minima pacing (LMP) can reduce the number of pulses and therefore the total electrical energy applied required to successfully terminate the underlying dynamics compared to ADP. Using different numerical models, initial conditions, and model parameters, the robustness of the effect is demonstrated. This study provides further evidence suggesting the significant potential of feedback for the termination of fibrillation.

Optogenetic Feedback Pacing
Cardiac optogenetics enables the manipulation of cellular functions using light, opening novel perspectives to study nonlinear cardiac function and control. We have investigated the efficacy of optical resonant feedback pacing to terminate ventricular tachyarrhythmias using numerical simulations and experiments in transgenic Langendorffperfused mouse hearts [6]. We show that the effectiveness of terminating cardiac arrhythmias using feedback pacing is superior to a single optical pulse, as illustrated in Fig. 8.16. At 50% success rate, the energy per pulse is 40 times lower than with a single pulse with 10 ms duration. We show that even at light intensities below the excitation threshold it is possible to terminate arrhythmias by spatiotemporal modulation of excitability, that induces a spiral wave drift and dissolving spiral wave core [7, 8].

References

1. T. Lilienkamp, U. Parlitz, S. Luther, Chaos 32, 121105 (2022)
2. D. Suth, S. Luther, T. Lilienkamp, Front. Netw. Physiol. 4, 1401661 (2024)
3. J. Steyer, T. Lilienkamp, S. Luther, U. Parlitz, Front. Netw. Physiol. 2, 1007585 (2023)
4. M. Aron, S. Luther, U. Parlitz, Front. Netw. Physiol. 5, 1572834 (2025)
5. M. Aron, T. Lilienkamp, S. Luther, U. Parlitz, Front. Netw. Physiol. 3, 1172454 (2023)
6. S. Hussaini, A. Mamyraiym Kyzy, J. Schröder-Schetelig et al., Chaos 34, 031103 (2024)
7. S. Hussaini, R. Majumder, V. Krinski, S. Luther, Pflügers Archiv: Eur. J. Phys. 475, 1453 (2023)
8. S. Hussaini, S.L. Lädke, J. Schröder-Schetelig et al., PLoS Comp. Biol. 19, e1011660 (2023)