A governing equation for rotor and wavelet number in human clinical ventricular fibrillation: Implications for sudden cardiac death,Heart Rhythm

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A governing equation for rotor and wavelet number in human clinical ventricular fibrillation: Implications for sudden cardiac death
Heart Rhythm ( IF 5.6 ) Pub Date : 2021-10-15 , DOI: 10.1016/j.hrthm.2021.10.008
Dhani Dharmaprani ₁ , Evan V Jenkins ₂ , Jing X Quah ₃ , Anandaroop Lahiri ₄ , Kathryn Tiver ₄ , Lewis Mitchell ₅ , Christopher P Bradley ₆ , Martin Hayward ₇ , David J Paterson ₈ , Peter Taggart ₉ , Richard H Clayton ₁₀ , Martyn P Nash ₆ , Anand N Ganesan ₃

Affiliation

College of Medicine and Public Health, Flinders University, Adelaide, Australia; College of Science and Engineering, Flinders University, Adelaide, Australia.
College of Medicine and Public Health, Flinders University, Adelaide, Australia.
College of Medicine and Public Health, Flinders University, Adelaide, Australia; Department of Cardiovascular Medicine, Flinders Medical Centre, Adelaide, Australia.
Department of Cardiovascular Medicine, Flinders Medical Centre, Adelaide, Australia.
School of Mathematical Sciences, University of Adelaide, Adelaide, Australia.
Auckland Bioengineering Institute, University of Auckland, Auckland, New Zealand.
University College London Hospitals NHS Foundation Trust, London, United Kingdom; UCLH Department of Cardiothoracic Surgery, London, United Kingdom.
Department of Physiology, Anatomy and Genetics, University of Oxford, Oxford, United Kingdom.
Institute of Cardiovascular Science, University College London, London, United Kingdom.
Insigneo Institute for in silico Medicine, University of Sheffield, Sheffield, United Kingdom.

Background

Ventricular fibrillation (VF) is characterized by multiple wavelets and rotors. No equation to predict the number of rotors and wavelets observed during fibrillation has been validated in human VF.

Objective

The purpose of this study was to test the hypothesis that a single equation derived from a Markov M/M/∞ birth-death process could predict the number of rotors and wavelets occurring in human clinical VF.

Methods

Epicardial induced VF (256-electrode) recordings obtained from patients undergoing cardiac surgery were studied (12 patients; 62 epochs). Rate constants for phase singularity (PS) (which occur at the pivot points of rotors) and wavefront (WF) formation and destruction were derived by fitting distributions to PS and WF interformation and lifetimes. These rate constants were combined in an M/M/∞ governing equation to predict the number of PS and WF in VF episodes. Observed distributions were compared to those predicted by the M/M/∞ equation.

Results

The M/M/∞ equation accurately predicted average PS and WF number and population distribution, demonstrated in all epochs. Self-terminating episodes of VF were distinguished from VF episodes requiring termination by a trend toward slower PS destruction, slower rates of PS formation, and a slower mixing rate of the VF process, indicated by larger values of the second largest eigenvalue modulus of the M/M/∞ birth-death matrix. The longest-lasting PS (associated with rotors) had shorter interactivation time intervals compared to shorter-lasting PS lasting <150 ms (∼1 PS rotation in human VF).

Conclusion

The M/M/∞ equation explains the number of wavelets and rotors observed, supporting a paradigm of VF based on statistical fibrillatory dynamics.

中文翻译：

人类临床心室颤动中转子和小波数的控制方程：对心源性猝死的影响

背景

心室颤动 (VF) 的特征在于多个小波和转子。尚未在人类 VF 中验证预测纤颤期间观察到的转子和小波数量的方程。

客观的

本研究的目的是检验从马尔可夫 M/M/∞ 出生-死亡过程导出的单个方程可以预测人类临床 VF 中发生的转子和小波数量的假设。

方法

研究了从接受心脏手术的患者获得的心外膜诱发 VF（256 个电极）记录（12 名患者；62 个时期）。相位奇异性 (PS)（发生在转子的枢轴点）和波前 (WF) 形成和破坏的速率常数是通过对 PS 和 WF 信息和寿命的分布进行拟合得出的。这些速率常数结合在 M/M/∞ 控制方程中，以预测 VF 发作中 PS 和 WF 的数量。将观察到的分布与 M/M/∞ 方程预测的分布进行比较。

结果

M/M/∞ 方程准确地预测了平均 PS 和 WF 数量和人口分布，在所有时期都得到了证明。VF 的自终止事件与需要终止的 VF 事件的区别在于 PS 破坏较慢、PS 形成速率较慢和 VF 过程混合速率较慢的趋势，由 M 的第二大特征值模数的较大值表示/M/∞ 生死矩阵。与持续时间小于 150 毫秒的持续时间较短的 PS（人类 VF 中约 1 PS 旋转）相比，持续时间最长的 PS（与转子相关）具有更短的交互时间间隔。