Defibrillation by teleportation terminates reentrant spiral-wave activity in an excitable medium with a single spatially designed low-energy stimulus: the stimulus is placed along the refractory contour joining a pair of wave singularities of opposite chirality (rotating in opposite senses) and instantaneously 'teleports' them toward each other so that they mutually annihilate. The mechanism and a complete stimulus-design recipe were demonstrated only in two-dimensional numerical simulations of cardiac tissue. The open problem is to carry this mechanism beyond that setting: to realize it experimentally in real excitable media with automated, real-time level-set identification and stimulus design, robust under noise, heterogeneity, and mapping-to-stimulus delays — ultimately in optogenetically modified cardiac monolayers and multi-spiral turbulent states — and to establish its three-dimensional generalization, where scroll-wave filaments organized by refractory and excitable surfaces replace contour-organized spiral pairs, including the required surface coverage, the detailed success/failure behavior, and a practicable stimulus implementation. A first experimental confirmation of teleportation and pairwise annihilation in a two-dimensional photosensitive Belousov–Zhabotinsky system with manually targeted perturbations appeared in 2024, but the automated protocol, cardiac validation, defibrillation of turbulent states, and the three-dimensional extension remain open.

Background

An excitable medium is a spatially extended system whose elements rest in a stable state but respond to super-threshold perturbations with a stereotyped excursion (activation followed by a refractory period during which no new excitation is possible). Cardiac tissue is a biological excitable medium: during ventricular fibrillation the normal orderly electrical activation breaks into turbulent wave patterns driven by rotating spiral waves (also called rotors), whose tips are phase singularities — points around which the phase of the excitation cycle winds by 2π2\pi. A classic laboratory model of excitable media is the Belousov–Zhabotinsky (BZ) reaction, an oscillating chemical reaction that, prepared in a thin layer, supports propagating excitation waves and spiral-wave reentry directly analogous to cardiac ones.

The only reliably deployed treatment for fibrillation is a strong, globally resetting electric shock (defibrillation), whose high energy can damage tissue and cause pain. Low-energy alternatives are under active study: low-energy anti-fibrillation pacing (LEAP, Luther et al. 2011) terminates fibrillation with sequences of far weaker pulses by exploiting the tissue's response heterogeneity. DeTal, Kaboudian, and Fenton (PNAS 2022; arXiv:2109.10850) proposed a topologically grounded alternative. They use a level-set description of the excitation state: the instantaneous boundaries (contours) between excited, refractory, and recovered regions organize the dynamics, and every phase singularity sits on the intersection of an 'excited' and a 'refractory' contour. The classic S1–S2 protocol for creating spiral waves works because a second stimulus (S2) placed on the refractory back of a first wave (S1) forces those contours to intersect, nucleating a singularity pair. DeTal et al. observed the time reverse: a stimulus that excites a strip covering the refractory contour joining two singularities of opposite chirality (whose phases wind in opposite senses) makes the singularities jump ('teleport') instantaneously along that contour toward one another, after which they attract and mutually annihilate. They derived a constructive recipe — apply a current IstimI_{\mathrm{stim}} to the voltage variable wherever the medium is not excited (f<0f<0, i.e. behind the excited front) and the refractory indicator function gg (a dimensionless function of the tissue model's state variables that is positive in refractory regions) satisfies ∣g∣<gth|g|<g_{\mathrm{th}}, giving the stimulus a finite thickness about the refractory back contour — and showed in two-dimensional simulations of four cardiac-tissue models of increasing complexity (the Karma, Beeler–Reuter, TNNP, and 41-variable OVVR human ventricular models) that a single so-designed stimulus eliminates all singularities of fibrillating, multi-spiral states at energies well below the defibrillation threshold, with IstimI_{\mathrm{stim}} or gthg_{\mathrm{th}} too small causing singularities to reform.

The authors' own conclusions identify what remains unproven. First, the demonstration is purely computational and two-dimensional: they propose optogenetically modified cardiac monolayers — layers of heart cells expressing light-gated ion channels, so that spatially patterned low-energy light can replace electrodes (optogenetics) — combined with optical mapping (camera-based, dye-mediated recording of the tissue's electrical activity) and established contour-determination methods, as the testbed that 'would allow for exact replication of our computational examples'; they argue on timing grounds (GPU contour analysis within the 1–2 ms mapping window) that real-time operation is feasible and that the targeting tolerates contour drift, but this is not demonstrated. Second, they generalize the mechanism only at the level of a topological argument: in three dimensions, spiral waves become scroll waves whose rotation is organized by one-dimensional singular filaments, and these are organized by refractory and excitable surfaces rather than contours; complete stimulation of the refractory surfaces joining filaments 'will eliminate the associated scroll waves, while partial stimulation results in the initiation of new waves' — a conjecture with no simulations, no surface-coverage analysis, and no experiment, which they suggest exploring in the BZ reaction in 3D. Whether the mechanism operates as predicted in real noisy, heterogeneous media, and whether it extends to scroll waves in three dimensions, is the open question.

Problem Statement

Establish whether defibrillation by teleportation — the topological single-designed-stimulus mechanism demonstrated by DeTal, Kaboudian, and Fenton in two-dimensional simulations — can be realized as a practical termination method for reentrant wave activity in real excitable media and extended to three dimensions. This single objective comprises three jointly supporting parts. (1) Experimental realization of the full protocol in a real two-dimensional excitable medium: automated identification of the level-set (excited/refractory) contours from measured data, real-time design of the stimulus covering the refractory contours joining opposite-chirality singularities, delivery of that single designed stimulus, and demonstration that it eliminates all singularities — including in turbulent multi-spiral states — with quantified robustness to experimental noise, medium heterogeneity, mapping-to-stimulus time delays, imperfect contour localization, and contour drift during processing. (2) Demonstration in cardiac tissue, the named target testbed: optogenetically modified cardiac monolayers with optical mapping, where the stimulus is spatially patterned low-energy light. (3) The three-dimensional generalization: for scroll waves whose one-dimensional singular filaments are organized by refractory and excitable surfaces, determine by computation and/or experiment whether complete stimulation of the refractory surfaces joining filaments eliminates the associated scroll waves while partial stimulation initiates new waves, quantify the surface coverage required, and identify practicable stimulus implementations. Part (1) without (3) would leave the mechanism a 2D-only curiosity for fibrillation, which is largely three-dimensional; (3) without (1)–(2) would leave it an untested numerical conjecture; together they answer whether teleportation is a viable basis for low-energy defibrillation and for the control of reentrant waves in excitable media generally.

References

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