Markov modeling of phase singularity interaction effects in human atrial and ventricular fibrillation.

Atrial and ventricular fibrillation (AF/VF) are characterized by the repetitive regeneration of topological defects known as phase singularities (PSs). The effect of PS interactions has not been previously studied in human AF and VF. We hypothesized that PS population size would influence the rate of PS formation and destruction in human AF and VF, due to increased inter-defect interaction. PS population statistics were studied in computational simulations (Aliev-Panfilov), human AF and human VF. The influence of inter-PS interactions was evaluated by comparison between directly modeled discrete-time Markov chain (DTMC) transition matrices of the PS population changes, and M/M/∞ birth-death transition matrices of PS dynamics, which assumes that PS formations and destructions are effectively statistically independent events. Across all systems examined, PS population changes differed from those expected with M/M/∞. In human AF and VF, the formation rates decreased slightly with PS population when modeled with the DTMC, compared with the static formation rate expected through M/M/∞, suggesting new formations were being inhibited. In human AF and VF, the destruction rates increased with PS population for both models, with the DTMC rate increase exceeding the M/M/∞ estimates, indicating that PS were being destroyed faster as the PS population grew. In human AF and VF, the change in PS formation and destruction rates as the population increased differed between the two models. This indicates that the presence of additional PS influenced the likelihood of new PS formation and destruction, consistent with the notion of self-inhibitory inter-PS interactions.

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

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.

Reconceptualising Atrial Fibrillation Using Renewal Theory: A Novel Approach to the Assessment of Atrial Fibrillation Dynamics.

Despite a century of research, the mechanisms of AF remain unresolved. A universal motif within AF research has been unstable re-entry, but this remains poorly characterised, with competing key conceptual paradigms of multiple wavelets and more driving rotors. Understanding the mechanisms of AF is clinically relevant, especially with regard to treatment and ablation of the more persistent forms of AF. Here, the authors outline the surprising but reproducible finding that unstable re-entrant circuits are born and destroyed at quasi-stationary rates, a finding based on a branch of mathematics known as renewal theory. Renewal theory may be a way to potentially unify the multiple wavelet and rotor theories. The renewal rate constants are potentially attractive because they are temporally stable parameters of a defined probability distribution (the exponential distribution) and can be estimated with precision and accuracy due to the principles of renewal theory. In this perspective review, this new representational architecture for AF is explained and placed into context, and the clinical and mechanistic implications are discussed.

The appropriateness of coronary investigation in myocardial injury and type 2 myocardial infarction (ACT-2): A randomized trial design.

BACKGROUND: Elevated troponin level findings among patients presenting with suspected acute coronary syndrome (ACS) or another intercurrent illness undeniably identifies patients at increased risk of mortality. Whilst enhancing our capacity to discriminate risk, the use of high-sensitivity troponin assays frequently identifies patients with myocardial injury (i.e. troponin rise without acute signs of myocardial ischemia) or type 2 myocardial infarction (T2MI; oxygen supply-demand imbalance). This leads to the clinically challenging task of distinguishing type 1 myocardial infarction (T1MI; coronary plaque rupture) from myocardial injury and T2MI in the context of concurrent acute illness. Diagnostic discernment in this context is crucial because MI classification has implications for further investigation and care. Early invasive management is of well-established benefit among patients with T1MI. However, the appropriateness of this investigation in the heterogeneous context of T2MI, where there is high competing mortality risk, remains unknown. Although coronary angiography in T2MI is advocated by some, there is insufficient evidence in existing literature to support this opinion as highlighted by current national guidelines. OBJECTIVE: The objective is to evaluate the clinical and economic impact of early invasive management with coronary angiography in T2MI in terms of all-cause mortality and cost effectiveness. DESIGN: This prospective, pragmatic, multicenter, randomized trial among patients with suspected supply demand ischemia leading to troponin elevation (n=1,800; T2MI [1,500], chronic myocardial injury [300]) compares the impact of invasive angiography (or computed tomography angiography as per local preference) within 5 days of randomization versus conservative management (with or without functional testing at clinician discretion) on all-cause mortality by 2 years. Randomized treatment allocation will be stratified by baseline estimated risk of mortality using the Acute Physiology, Age, and Chronic Health Evaluation (APACHE) III risk score. Cost-effectiveness will be evaluated by follow-up on clinical events, quality of life, and resource utilization over 24 months. SUMMARY: Ascertaining the most appropriate first-line investigative strategy for these commonly encountered high-risk T2MI patients in a randomized comparative study will be pivotal in informing evidence-based guidelines that lead to better patient and health care outcomes.