Causal Scale of Rotors in a Cardiac System

Ashikaga, Hiroshi; Prieto‐Castrillo, Francisco; Kawakatsu, Mari; Dehghani, Nima

doi:10.3389/fphy.2018.00030

Cited by 8 publications

(9 citation statements)

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“…Stochastic renormalization. First, to construct a series of robust and minimal macro-scale descriptions of the system, we generated a renormalization group of the system by a series of spatial and temporal transformation including coarse-graining and rescaling (13). Multi-lead mapping of the atria in sinus rhythm and AF was conducted by a 64-lead basket catheter (50 mm or 60 mm; Abbott Electrophysiology, Menlo Park, California; Figure 1A), each atrium at a time (Figure 1B).…”

Section: Resultsmentioning

confidence: 99%

Causal Scale Shift Associated with Phase Transition to Human Atrial Fibrillation

Ashikaga,

Aronis,

Tao

et al. 2018

Preprint

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An example of phase transition in natural complex systems is the qualitative and sudden change in the heart rhythm between sinus rhythm and atrial fibrillation (AF), the most common irregular heart rhythm in humans. While the system behavior is centrally controlled by the behavior of the sinoatrial node in sinus rhythm, the macro-scale collective behavior of the heart causes the micro-scale behavior in AF. To quantitatively analyze this causation shift associated with phase transition in human heart, we evaluated the causal architecture of the human cardiac system using the time series of multi-lead intracardiac unipolar electrograms in a series of spatiotemporal scales by generating a stochastic renormalization group. We found that the phase transition between sinus rhythm and AF is associated with a significant shift of the peak causation from macroscopic to microscopic scales. Causal architecture analysis provides a quantitative tool to improve our understanding of causality in phase transitions in other natural and social complex systems.Complex systems | Information theory | Renormalization group | Cardiac dynamics P hase transitions between ordered and disordered states often reveal critical features of the underlying natual and social complex systems comprised of large numbers of components (1). One example of phase transition in natural complex systems is the qualitative and sudden change in the heart rhythm between sinus rhythm and atrial fibrillation (AF) (2), the most common irregular heart rhythm in human beings (3). During sinus rhythm, the system behavior at the macroscopic scale is relatively simple, because it is centrally controlled by the behavior of the sinoatrial node. In contrast, as soon as the heart undergoes an order-disorder phase transition to AF, complex system behaviors emerge where the macro-scale collective behavior of the heart causes the micro-scale behavior ('supersedence'). The shift of causation from the centrally controlled sinus rhythm to AF, which controls the behaviors of individual cardiomyocytes to maintain itself, is clinically observable in the phenomenon called 'AF begets AF', where a longer duration of pacing-maintained AF results in a longer maintenance of AF after cessation of pacing (4). Although this causation shift associated with phase transition to human AF has been qualitatively described, it has never been documented in a quantitative fashion.The intra-and inter-scale interactions of multi-scale complex systems can be mathematically quantified by information theory (5). In the cardiac system, we have previously shown that information-theoretic metrics such as mutual information (6) and transfer entropy (7) can quantify the interactions between micro-scale components (8), and the interactions between microand macro-scale behaviors during fibrillation (9). We have also shown that those information-theoretic metrics can quantify how the interactions among micro-scale components alter the macro-scale collective behavior during fibrillation (10) or cause an order-d...

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Section: Resultsmentioning

confidence: 99%

Causal Scale Shift Associated with Phase Transition to Human Atrial Fibrillation

Ashikaga,

Aronis,

Tao

et al. 2018

Preprint

Self Cite

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“…In each component, we computed the time series of transmembrane potential for 10 seconds excluding the stimulation period with a time step of 0.1 msec, which was subsequently downsampled at a sampling frequency of 1,000 Hz [17]. The rotors were defined as the phase singularities of the phase map as described [13]. To approximate clinical recordings, we converted the transmembrane potential derived from the model to unipolar and subsequently to bipolar electrogram (Figure 1B) using the 64 × 64 lattice [18].…”

Section: Methodsmentioning

confidence: 99%

“…We generated a renormalization group of the system by a series of spatial and temporal transformation including coarse-graining and rescaling of the original microscopic description of the system (Figure 1C) [12]. We coarsegrained the system spatially and temporally with decimation by a factor of 2.…”

Section: Renormalization Groupmentioning

confidence: 99%

“…The aim of the study was to describe the complex interactions among cardiac components during spiral waves at multiple scales. To accomplish the aim, we applied iterated coarse-graining and rescaling [11] to the microscopic description of the cardiac system with spiral waves to generate a renormalization group in a series of spatiotemporal scales [12,13]. We hypothesized that the LCS of information flow underlying spiral waves are scale-invariant.…”

Section: Introductionmentioning

confidence: 99%

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Scale-invariant structures of spiral waves

Sohn

Aronis

Ashikaga

2019

Computers in Biology and Medicine

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Background: Spiral waves are considered to be one of the potential mechanisms that maintain complex arrhythmias such as atrial and ventricular fibrillation. The aim of the present study was to quantify the complex dynamics of spiral waves as the organizing manifolds of information flow at multiple scales. Method: We simulated spiral waves using a numerical model of cardiac excitation in a two-dimensional (2-D) lattice. We created a renormalization group by coarse graining and re-scaling the original time series in multiple spatiotemporal scales, and quantified the Lagrangian coherent structures (LCS) of the information flow underlying the spiral waves. To quantify the scale-invariant structures, we compared the value of the finite-time Lyapunov exponent between the corresponding components of the 2-D lattice in each spatiotemporal scale of the renormalization group with that of the original scale. Results: Both the repelling and the attracting LCS changed across the different spatial and temporal scales of the renormalization group. However, despite the change across the scales, some LCS were scale-invariant. The patterns of those scale-invariant structures were not obvious from the trajectory of the spiral waves based on voltage mapping of the lattice. Conclusions: Some Lagrangian coherent structures of information flow underlying spiral waves are preserved across multiple spatiotemporal scales.

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“…Burr weaves in concepts from physics, discussing the bidirectional feedback between field and particle. This paper (and Burr's overall body of work) is focused on bioelectric fields as a specific example, but this is (as I'm sure he realized) a much bigger issue, currently playing out in state-of-the-art discussions about agent-based models and downward causation from global "virtual governors" and global, distributed dynamics that emerge from relatively simple local rules governing proteins, subcellular structures, cells, and tissues (Pezzulo and Levin 2016;Torday and Miller 2016;Walker et al 2016;Albantakis et al 2017;Flack 2017;Ashikaga et al 2018;Juel et al 2019).…”

Section: The Electro-dynamic Theory Of Lifementioning

confidence: 99%

Revisiting Burr and Northrop’s “The Electro-Dynamic Theory of Life” (1935)

Levin

2020

Biol Theory

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Harold Saxton Burr was a biologist working throughout the 1930s-1950s on an important set of problems related to biological organization and the origin of complex living forms. He was a profound thinker, suggesting a complementary focus on field concepts in addition to the emphasis on particle models and integrating concepts from physics and philosophy in his work. He developed innovations in electrophysiological technique and used them to perform a wide experimental survey of bioelectricity in normal and pathological growth. Here, I briefly review his classic paper with philosopher F. S. C. Northrop, "The Electro-Dynamic Theory of Life," in the context of advances in this field over the last few decades. Based on recent progress, it is now clear that Burr was a prescient and visionary thinker. His main hypothesis, that bioelectric gradients serve as prepatterns guiding morphogenesis, has been confirmed using modern molecular physiology, as have his ideas about the place of cancer and the nervous system in the question of biological organization. With limited technology but deep insight, he derived insights that anticipated many modern discoveries. Even more importantly, Burr's view of bioelectricity as a convenient entry point for rigorous investigation of the broader question of self-organizing properties of life highlights a frontier of inquiry that awaits today's researchers. Burr and Northrop's "The Electro-Dynamic Theory of Life," originally published in the Quarterly Review of Biology (10(3):322-333, 1935), is available as supplementary material in the online version of this essay. Keywords Bioelectricity • Development • Embryogenesis • Voltage Talent hits a target no one else can hit; genius hits a target no one else can see.

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Causal Scale of Rotors in a Cardiac System

Cited by 8 publications

References 72 publications

Causal Scale Shift Associated with Phase Transition to Human Atrial Fibrillation

Causal Scale Shift Associated with Phase Transition to Human Atrial Fibrillation

Scale-invariant structures of spiral waves

Revisiting Burr and Northrop’s “The Electro-Dynamic Theory of Life” (1935)

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