Observable Atrial and Ventricular Fibrillation Episode Durations Are Conformant With a Power Law Based on System Size and Spatial Synchronization
Bibliographic record
Abstract
BACKGROUND: Atrial fibrillation (AF) and ventricular fibrillation (VF) episodes exhibit varying durations, with some spontaneously ending quickly while others persist. A quantitative framework to explain episode durations remains elusive. We hypothesized that observable self-terminating AF and VF episode lengths, whereby durations are known, would conform with a power law based on the ratio of system size and correlation length ( <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mstyle displaystyle="false"> <mml:msup> <mml:mrow/> <mml:mrow> <mml:mi>L</mml:mi> </mml:mrow> </mml:msup> <mml:mrow> <mml:mo>/</mml:mo> </mml:mrow> <mml:msub> <mml:mrow/> <mml:mrow> <mml:mi>ξ</mml:mi> </mml:mrow> </mml:msub> <mml:mo stretchy="false">)</mml:mo> </mml:mstyle> </mml:math> . METHODS: Using data from computer simulations (2-dimensional sheet and 3-dimensional left-atrial), human ischemic VF recordings (256-electrode sock, n=12 patients), and human AF recordings (64-electrode basket-catheter, n=9 patients; 16-electrode high definition-grid catheter, n=42 patients), conformance with a power law was assessed using the Akaike information criterion, Bayesian information criterion, coefficient of determination (R 2 , significance= P <0.05) and maximum likelihood estimation. We analyzed fibrillatory episode durations and <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mstyle displaystyle="false"> <mml:msup> <mml:mrow/> <mml:mrow> <mml:mi>L</mml:mi> </mml:mrow> </mml:msup> <mml:mrow> <mml:mo>/</mml:mo> </mml:mrow> <mml:msub> <mml:mrow/> <mml:mrow> <mml:mi>ξ</mml:mi> </mml:mrow> </mml:msub> </mml:mstyle> </mml:math> , computed by taking the ratio between system size ( <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mstyle displaystyle="false"> <mml:mi>L</mml:mi> </mml:mstyle> </mml:math> , chamber/simulation size) and correlation length (xi, estimated from pairwise correlation coefficients over electrode/node distance). RESULTS: In all computer models, the relationship between episode durations and <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mstyle displaystyle="false"> <mml:msup> <mml:mrow/> <mml:mrow> <mml:mi>L</mml:mi> </mml:mrow> </mml:msup> <mml:mrow> <mml:mo>/</mml:mo> </mml:mrow> <mml:msub> <mml:mrow/> <mml:mrow> <mml:mi>ξ</mml:mi> </mml:mrow> </mml:msub> </mml:mstyle> </mml:math> was conformant with a power law (Aliev-Panfilov R 2 : 0.90, P <0.001; Courtemanche R 2 : 0.91, P <0.001; Luo-Rudy R 2 : 0.61, P <0.001). Observable clinical AF/VF durations were also conformant with a power law relationship (VF R 2 : 0.86, P <0.001; AF basket R 2 : 0.91, P <0.001; AF grid R 2 : 0.92, P <0.001). <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mstyle displaystyle="false"> <mml:msup> <mml:mrow/> <mml:mrow> <mml:mi>L</mml:mi> </mml:mrow> </mml:msup> <mml:mrow> <mml:mo>/</mml:mo> </mml:mrow> <mml:msub> <mml:mrow/> <mml:mrow> <mml:mi>ξ</mml:mi> </mml:mrow> </mml:msub> <mml:mtext/> </mml:mstyle> </mml:math> also differentiated between self-terminating and sustained episodes of AF and VF ( P <0.001; all systems), as well as paroxysmal versus persistent AF ( P <0.001). In comparison, other electrogram metrics showed no statistically significant differences (dominant frequency, Shannon Entropy, mean voltage, peak-peak voltage; P >0.05). CONCLUSIONS: Observable fibrillation episode durations are conformant with a power law based on system size and correlation length.
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How this classification was reachedexpand
Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one teacher head, not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".