Observable Atrial and Ventricular Fibrillation Episode Durations Are Conformant With a Power Law Based on System Size and Spatial Synchronization.

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 ([Formula: see text]. 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 (R2, significance=P<0.05) and maximum likelihood estimation. We analyzed fibrillatory episode durations and [Formula: see text], computed by taking the ratio between system size ([Formula: see text], 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 [Formula: see text] was conformant with a power law (Aliev-Panfilov R2: 0.90, P<0.001; Courtemanche R2: 0.91, P<0.001; Luo-Rudy R2: 0.61, P<0.001). Observable clinical AF/VF durations were also conformant with a power law relationship (VF R2: 0.86, P<0.001; AF basket R2: 0.91, P<0.001; AF grid R2: 0.92, P<0.001). [Formula: see text] 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.

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.

The inspection paradox: An important consideration in the evaluation of rotor lifetimes in cardiac fibrillation.

Background and Objective: Renewal theory is a statistical approach to model the formation and destruction of phase singularities (PS), which occur at the pivots of spiral waves. A common issue arising during observation of renewal processes is an inspection paradox, due to oversampling of longer events. The objective of this study was to characterise the effect of a potential inspection paradox on the perception of PS lifetimes in cardiac fibrillation. Methods: A multisystem, multi-modality study was performed, examining computational simulations (Aliev-Panfilov (APV) model, Courtmanche-Nattel model), experimentally acquired optical mapping Atrial and Ventricular Fibrillation (AF/VF) data, and clinically acquired human AF and VF. Distributions of all PS lifetimes across full epochs of AF, VF, or computational simulations, were compared with distributions formed from lifetimes of PS existing at 10,000 simulated commencement timepoints. Results: In all systems, an inspection paradox led towards oversampling of PS with longer lifetimes. In APV computational simulations there was a mean PS lifetime shift of +84.9% (95% CI, ± 0.3%) (p < 0.001 for observed vs overall), in Courtmanche-Nattel simulations of AF +692.9% (95% CI, ±57.7%) (p < 0.001), in optically mapped rat AF +374.6% (95% CI, ± 88.5%) (p = 0.052), in human AF mapped with basket catheters +129.2% (95% CI, ±4.1%) (p < 0.05), human AF-HD grid catheters 150.8% (95% CI, ± 9.0%) (p < 0.001), in optically mapped rat VF +171.3% (95% CI, ±15.6%) (p < 0.001), in human epicardial VF 153.5% (95% CI, ±15.7%) (p < 0.001). Conclusion: Visual inspection of phase movies has the potential to systematically oversample longer lasting PS, due to an inspection paradox. An inspection paradox is minimised by consideration of the overall distribution of PS lifetimes.

Role of interatrial conduction in atrial fibrillation: Mechanistic insights from renewal theory-based fibrillatory dynamic analysis.

Background: Interatrial conduction has been postulated to play an important role in atrial fibrillation (AF). The pathways involved in interatrial conduction during AF remain incompletely defined. Objective: We recently showed physiological assessment of fibrillatory dynamics could be performed using renewal theory, which determines rates of phase singularity formation (λf) and destruction (λd). Using the renewal approach, we aimed to understand the role of the interatrial septum and other electrically coupled regions during AF. Method: RENEWAL-AF is a prospective multicenter observational study recruiting AF ablation patients (ACTRN 12619001172190). We studied unipolar electrograms obtained from 16 biatrial locations prior to ablation using a 16-electrode Advisor HD Grid catheter. Renewal rate constants λf and λd were calculated, and the relationships between these rate constants in regions of interatrial connectivity were examined. Results: Forty-one AF patients (28.5% female) were recruited. A positive linear correlation was observed between λf and λd (1) across the interatrial septum (λf r2 = 0.5, P < .001, λd r2 = 0.45, P < .001), (2) in regions connected by the Bachmann bundle (right atrial appendage-left atrial appendage λf r2 = 0.29, P = .001; λd r2 = 0.2, P = .008), and (3) across the inferior interatrial routes (cavotricuspid isthmus-left atrial septum λf r2 = 0.67, P < .001; λd r2 = 0.55, P < .001). Persistent AF status and left atrial volume were found to be important effect modifiers of the degree of interatrial renewal rate statistical correlation. Conclusion: Our findings support the role of interseptal statistically determined electrical disrelation in sustaining AF. Additionally, renewal theory identified preferential conduction through specific interatrial pathways during fibrillation. These findings may be of importance in identifying clinically significant targets for ablation in AF patients.

Toward a Better Understanding of Muscle Microvascular Perfusion During Exercise in Patients With Peripheral Artery Disease: The Effect of Lower-Limb Revascularization.

PURPOSE: Leg muscle microvascular blood flow (perfusion) is impaired in response to maximal exercise in patients with peripheral artery disease (PAD); however, during submaximal exercise, microvascular perfusion is maintained due to a greater increase in microvascular blood volume compared with that seen in healthy adults. It is unclear whether this submaximal exercise response reflects a microvascular impairment, or whether it is a compensatory response for the limited conduit artery flow in PAD. Therefore, to clarify the role of conduit artery blood flow, we compared whole-limb blood flow and skeletal muscle microvascular perfusion responses with exercise in patients with PAD (n=9; 60±7 years) prior to, and following, lower-limb endovascular revascularization. MATERIALS AND METHODS: Microvascular perfusion (microvascular volume × flow velocity) of the medial gastrocnemius muscle was measured before and immediately after a 5 minute bout of submaximal intermittent isometric plantar-flexion exercise using contrast-enhanced ultrasound imaging. Exercise contraction-by-contraction whole-leg blood flow and vascular conductance were measured using strain-gauge plethysmography. RESULTS: With revascularization there was a significant increase in whole-leg blood flow and conductance during exercise (p<0.05). Exercise-induced muscle microvascular perfusion response did not change with revascularization (pre-revascularization: 3.19±2.32; post-revascularization: 3.89±1.67 aU.s-1; p=0.38). However, the parameters that determine microvascular perfusion changed, with a reduction in the microvascular volume response to exercise (pre-revascularization: 6.76±3.56; post-revascularization: 2.42±0.69 aU; p<0.01) and an increase in microvascular flow velocity (pre-revascularization: 0.25±0.13; post-revascularization: 0.59±0.25 s-1; p=0.02). CONCLUSION: These findings suggest that patients with PAD compensate for the conduit artery blood flow impairment with an increase in microvascular blood volume to maintain muscle perfusion during submaximal exercise. CLINICAL IMPACT: The findings from this study support the notion that the impairment in conduit artery blood flow in patients with PAD leads to compensatory changes in microvascular blood volume and flow velocity to maintain muscle microvascular perfusion during submaximal leg exercise. Moreover, this study demonstrates that these microvascular changes are reversed and become normalized with successful lower-limb endovascular revascularization.

Understanding the origins of the basic equations of statistical fibrillatory dynamics.

The mechanisms governing cardiac fibrillation remain unclear; however, it most likely represents a form of spatiotemporal chaos with conservative system dynamics. Renewal theory has recently been suggested as a statistical formulation with governing equations to quantify the formation and destruction of wavelets and rotors in fibrillatory dynamics. In this perspective Review, we aim to explain the origin of the renewal theory paradigm in spatiotemporal chaos. The ergodic nature of pattern formation in spatiotemporal chaos is demonstrated through the use of three chaotic systems: two classical systems and a simulation of cardiac fibrillation. The logistic map and the baker's transformation are used to demonstrate how the apparently random appearance of patterns in classical chaotic systems has macroscopic parameters that are predictable in a statistical sense. We demonstrate that the renewal theory approach developed for cardiac fibrillation statistically predicts pattern formation in these classical chaotic systems. Renewal theory provides governing equations to describe the apparently random formation and destruction of wavelets and rotors in atrial fibrillation (AF) and ventricular fibrillation (VF). This statistical framework for fibrillatory dynamics provides a holistic understanding of observed rotor and wavelet dynamics and is of conceptual significance in informing the clinical and mechanistic research of the rotor and multiple-wavelet mechanisms of AF and VF.

Electrogram analysis to detect cathodal and anodal capture in left ventricular cardiac resynchronization pacing leads.

AIMS: Our study analyzed cardiac electrograms (EGMs) to identify characteristics for detecting cathodal, anodal, or cathodal-anodal (simultaneous) capture in left ventricular (LV) quadripolar pacing leads of cardiac resynchronization therapy (CRT) patients. The relationship between these EGM characteristics and the electrocardiogram (ECG) was also examined. METHODS: We performed a retrospective analysis of 54 bipolar pacing configurations across nine patients with implanted CRT devices and quadripolar leads who had undergone a 12 lead ECG optimization. Three pacing tests (cathode unipolar, anode unipolar, and bipolar) per bipolar pair were performed, examining ECG and EGM morphology changes accompanying each test and any transitions of morphology or amplitude during voltage stepdown. RESULTS: During the cathode and anode unipolar pacing tests, the EGM was biphasic (negative/positive) or monophasic (positive) in 52/53 (98%), and biphasic (positive/negative) or monophasic (negative) in 50/51 (98%), respectively. During bipolar LV capture threshold testing, 30 bipolar pairs displayed a sudden increase in EGM amplitude (median 9.4 mV, interquartile range [7-14 mV]) when transitioning from cathodal-anodal capture to cathodal or anodal capture. Ninety percent of these EGM transitions had a corresponding simultaneous change in ECG, while 10% had no ECG changes. Two patients demonstrated "quad-site" capture on their quadripolar lead with multipoint pacing enabled and cathodal-anodal capture from each stimulus. CONCLUSION: EGM characteristics during LV pacing tests can reliably detect cathodal, anodal, or cathodal-anodal capture, with greater sensitivity than 12 lead ECG changes. Integration of EGM analysis into routine CRT device follow up can be performed easily and may have implications for CRT efficacy.

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.

WITHDRAWN: Impact of Racial Differences on the Epidemiology and Clinical Outcomes of Atrial Fibrillation

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Spatial concentration and distribution of phase singularities in human atrial fibrillation: Insights for the AF mechanism.

BACKGROUND: Atrial fibrillation (AF) is characterized by the repetitive regeneration of unstable rotational events, the pivot of which are known as phase singularities (PSs). The spatial concentration and distribution of PSs have not been systematically investigated using quantitative statistical approaches. OBJECTIVES: We utilized a geospatial statistical approach to determine the presence of local spatial concentration and global clustering of PSs in biatrial human AF recordings. METHODS: 64-electrode conventional basket (~5 min, n = 18 patients, persistent AF) recordings were studied. Phase maps were produced using a Hilbert-transform based approach. PSs were characterized spatially using the following approaches: (i) local "hotspots" of high phase singularity (PS) concentration using Getis-Ord Gi* (Z ≥ 1.96, P ≤ .05) and (ii) global spatial clustering using Moran's I (inverse distance matrix). RESULTS: Episodes of AF were analyzed from basket catheter recordings (H: 41 epochs, 120 000 s, n = 18 patients). The Getis-Ord Gi* statistic showed local PS hotspots in 12/41 basket recordings. As a metric of spatial clustering, Moran's I showed an overall mean of 0.033 (95% CI: 0.0003-0.065), consistent with the notion of complete spatial randomness. CONCLUSION: Using a systematic, quantitative geospatial statistical approach, evidence for the existence of spatial concentrations ("hotspots") of PSs were detectable in human AF, along with evidence of spatial clustering. Geospatial statistical approaches offer a new approach to map and ablate PS clusters using substrate-based approaches.

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 Association Between Contrast-Enhanced Ultrasound and Near-Infrared Spectroscopy-Derived Measures of Calf Muscle Microvascular Responsiveness in Older Adults.

BACKGROUND AND AIM: Contrast-enhanced ultrasound (CEUS) measures of post-occlusion skeletal muscle microvascular responsiveness demonstrate the microvascular dysfunction associated with ageing and age-related disease. However, the accessibility of CEUS is limited by the need for intravenous administration of ultrasound contrast agents and sophisticated imaging analysis. Alternative methods are required for the broader assessment of microvascular dysfunction in research and clinical settings. Therefore, we aimed to evaluate the level of association and agreement between CEUS and near-infrared spectroscopy (NIRS)-derived measures of post-occlusion skeletal muscle microvascular responsiveness in older adults. METHODS: During supine rest, participants (n=15, 67±11 years) underwent 5 minutes of thigh cuff-occlusion (200 mmHg). Post-occlusion CEUS measures of calf muscle microvascular responsiveness were made, including time to 95% peak acoustic intensity (TTP95 AI) and the rate of rise (slope AI). Simultaneous measures, including time to 95% peak oxygenated haemoglobin (TTP95 O2Hb) and slope O2Hb, were made using continuous-wave NIRS in the same muscle region. RESULTS: There were strong correlations between TTP95 measures derived from CEUS and NIRS (r=0.834, p=<0.001) and the corresponding measures of slope (r=0.735, p=0.004). The limits of agreement demonstrated by Bland Altman plot analyses for CEUS and NIRS-derived measures of TTP95 (-9.67-1.98 s) and slope (-1.29-5.23%. s-1) were smaller than the minimum differences expected in people with microvascular dysfunction. CONCLUSIONS: The strong correlations and level of agreement in the present study support the use of NIRS as a non-invasive, portable and cost-effective method for assessing post-occlusion skeletal muscle microvascular responsiveness in older adults.

Atrial fibrosis and substrate based characterization in atrial fibrillation: Time to move forwards.

Atrial fibrillation (AF) is the most commonly encountered cardiac arrhythmia in clinical practice. However, current therapeutic interventions for atrial fibrillation have limited clinical efficacy as a consequence of major knowledge gaps in the mechanisms sustaining atrial fibrillation. From a mechanistic perspective, there is increasing evidence that atrial fibrosis plays a central role in the maintenance and perpetuation of atrial fibrillation. Electrophysiologically, atrial fibrosis results in alterations in conduction velocity, cellular refractoriness, and produces conduction block promoting meandering, unstable wavelets and micro-reentrant circuits. Clinically, atrial fibrosis has also linked to poor clinical outcomes including AF-related thromboembolic complications and arrhythmia recurrences post catheter ablation. In this article, we review the pathophysiology behind the formation of fibrosis as AF progresses, the role of fibrosis in arrhythmogenesis, surrogate markers for detection of fibrosis using cardiac magnetic resonance imaging, echocardiography and electroanatomic mapping, along with their respective limitations. We then proceed to review the current evidence behind therapeutic interventions targeting atrial fibrosis, including drugs and substrate-based catheter ablation therapies followed by the potential future use of electro phenotyping for AF characterization to overcome the limitations of contemporary substrate-based methodologies.

Atrial fibrillation burden: an update-the need for a CHA2DS2-VASc-AFBurden score.

Atrial fibrillation (AF) is an established independent risk factor for stroke. Current guidelines regard AF as binary; either present or absent, with the decision for anti-coagulation driven by clinical variables alone. However, there are increasing data to support a biological gradient of AF burden and stroke risk, both in clinical and non-clinical AF phenotypes. As such, this raises the concept of combining AF burden assessment with a clinical risk score to refine and individualize the assessment of stroke risk in AF-the CHA2DS2VASc-AFBurden score. We review the published data supporting a biological gradient to try and construct a putative schema of risk attributable to AF burden.

Influence of cuff-occlusion duration on contrast-enhanced ultrasound assessments of calf muscle microvascular blood flow responsiveness in older adults.

NEW FINDINGS: What is the central question of the study? Cuff-occlusion duration may influence contrast-enhanced ultrasound (CEUS) assessments of skeletal muscle microvascular blood flow responsiveness: what are the effects of 1, 3 and 5 min cuff-occlusion on the magnitude and reliability of calf muscle microvascular blood flow responsiveness in older adults? What is the main finding and its importance? Calf muscle microvascular blood flow responsiveness was enhanced following 5 min cuff-occlusion compared with 1 min. The reliability of post-occlusion CEUS measurements was also improved following 5 min occlusion. The use of a standardized 5 min occlusion period should therefore be considered in future studies and clinical practice. ABSTRACT: Contrast-enhanced ultrasound (CEUS) is increasingly used in assessments of skeletal muscle microvascular blood flow responsiveness. In response to limb cuff-occlusion, some studies have reported significant impairments in CEUS measurements of microvascular blood flow in older adults with cardiovascular or metabolic disease, whereas others have failed to detect significant between-group differences, which has brought the reliability of the technique into question. In the absence of a standardized CEUS protocol, there is variance in the duration of cuff-occlusion used, which is likely to influence post-occlusion measurements of muscle microvascular blood flow. We aimed to determine the effect of cuff-occlusion duration by comparing the magnitude and reliability of CEUS measurements of calf muscle microvascular blood flow responsiveness in older adults (n = 15, 67 ± 11 years) following 1, 3 and 5 min occlusion periods. Microvascular blood flow (= microvascular volume × microvascular velocity) within the calf muscle was measured using real-time destruction-replenishment CEUS. Measurements were made following thigh cuff-occlusion (200 mmHg) periods of 1, 3 and 5 min in a random order. Microvascular blood flow was higher following 3 min (3.71 ± 1.46 aU s-1 ) and 5 min (3.47 ± 1.48 aU s-1 ) compared with 1 min (2.42 ± 1.27 aU s-1 , P = 0.002), which corresponded with higher microvascular volumes after 3 and 5 min compared with 1 min. Reliability was good following 5 min (intraclass correlation coefficient (ICC) 0.49) compared with poor following 1 min (ICC 0.34) and 3 min (ICC 0.35). This study demonstrates that the magnitude and reliability of calf muscle microvascular responsiveness is enhanced using a 5 min cuff-occlusion protocol compared with 1 min in older adults.

Relationship between coronary microvascular dysfunction and left ventricular diastolic function in patients with chest pain and unobstructed coronary arteries.

BACKGROUD: Diastolic dysfunction (DD) is reported to affect up to 35% of the adult general population. The consequence of progressive DD is heart failure with preserved ejection fraction (HFpEF). Coronary microvascular dysfunction (CMD) has been suggested as one of the pathologic mechanisms leading to HFpEF. We investigated whether there was an association between coronary microvascular function and echocardiographic indices of left ventricular diastolic function at rest in patients with chest pain and unobstructed coronary arteries (CPUCA). METHODS: This retrospective observational study recruited patients referred to cardiology clinics assessment of chest pain who subsequently underwent assessment via CT coronary angiogram (CTA). Coronary microvascular dysfunction was determined by myocardial blood flow reserve (MBFR; <2.0) using myocardial contrast echocardiography. Echocardiographic indices of diastolic function (septal mitral annular e'; septal mitral annular E/e', E/A ratio) were measured from baseline transthoracic echocardiogram. RESULTS: 149 patients (52% men) with a mean age 59.7(9.5) years were recruited. Mean (standard deviation) MBFR was 2.2 (0.51). 37% (55/149) had MBFR < 2.0. Median [interquartile range] septal mitral annular e' velocity and septal mitral annular E/e' were 7.6 cm/s [6.2, 8.9] and 9.5 [7.5, 10.8], respectively. Univariate regression analysis showed only age was a significant predictor of increasing septal mitral annular E/e' (ß = +0.20 95% CI 0.13, +0.28, P < .001) but not MBFR. Multivariable analysis also showed no association between these septal mitral annular E/e' and MBFR after adjustment for cardiovascular risk factors. CONCLUSION: There was no relationship found between echocardiographic indices of left ventricular diastolic function and coronary microvascular function at rest.

Prospective cross-sectional study using Poisson renewal theory to study phase singularity formation and destruction rates in atrial fibrillation (RENEWAL-AF): Study design.

BACKGROUND: Unstable functional reentrant circuits known as rotors have been consistently observed in atrial fibrillation and are mechanistically believed critical to the maintenance of the arrhythmia. Recently, using a Poisson renewal theory-based quantitative framework, we have demonstrated that rotor formation (λf) and destruction rates (λd) can be measured using in vivo electrophysiologic data. However, the association of λf and λd with clinical, electrical, and structural markers of atrial fibrillation phenotype is unknown. METHODS: RENEWAL-AF is a multicenter prospective cross-sectional study recruiting adult patients with paroxysmal or persistent atrial fibrillation undergoing clinically indicated catheter ablation. Patients will undergo intraprocedural electrophysiologic atrial fibrillation mapping, with λf and λd to be determined from 2-minute unipolar electrogram recordings acquired before ablation. The primary objective will be to determine the association of λf and λd as markers of fibrillatory dynamics with clinical, electrical, and structural markers of atrial fibrillation clinical phenotype, measured by preablation transthoracic echocardiogram and cardiac magnetic resonance imaging. An exploratory objective is the noninvasive assessment of λf and λd using surface ECG characteristics via a machine learning approach. RESULTS: Not applicable. CONCLUSION: This pilot study will provide insight into the correlation between λf/λd with clinical, electrophysiological, and structural markers of atrial fibrillation phenotype and provide a foundation for the development of noninvasive assessment of λf/λd using surface ECG characteristics will help expand the use of λf/λd in clinical practice.

An Experimental Series Investigating the Effects of Hyperinsulinemic Euglycemia on Myocardial Blood Flow Reserve in Healthy Individuals and on Myocardial Perfusion Defect Size following ST-Segment Elevation Myocardial Infarction.

BACKGROUND: Incomplete restoration of myocardial blood flow (MBF) is reported in up to 30% of ST-segment elevation myocardial infarction (STEMI) despite prompt mechanical revascularization. Experimental hyperinsulinemic euglycemia (HE) increases MBF reserve (MBFR). If fully exploited, this effect may also improve MBF to ischemic myocardium. Using insulin-dextrose infusions to induce HE, we conducted four experiments to determine (1) how insulin infusion duration, dose, and presence of insulin resistance affect MBFR response; and (2) the effect of an insulin-dextrose infusion given immediately following revascularization of STEMI on myocardial perfusion. METHODS: The MBFR was determined using myocardial contrast echocardiography. Experiment 1 (insulin duration): 12 participants received an insulin-dextrose or saline infusion for 120 minutes. MBFR was measured at four time intervals during infusion. Experiment 2 (insulin dose): 22 participants received one of three insulin doses (0.5, 1.5, 3.0 mU/kg/minute) for 60 minutes. Baseline and 60-minute MBFRs were determined. Experiment 3 (insulin resistance): five metabolic syndrome and six type 2 diabetes (T2DM) participants received 1.5 mU/kg/minute of insulin-dextrose for 60 minutes. Baseline and 60-minute MBFRs were determined. Experiment 4 (STEMI): following revascularization for STEMI, 20 patients were randomized to receive either 1.5 mU/kg/minute insulin-dextrose infusion for 120 minutes or standard care. Myocardial contrast echocardiography was performed at four time intervals to quantify percentage contrast defect length. RESULTS: Experiment 1: MBFR increased with time through to 120 minutes in the insulin-dextrose group and did not change in controls. Experiment 2: compared with baseline, MBFR increased in the 1.5 (2.42 ± 0.39 to 3.25 ± 0.77, P = .002), did not change in the 0.5, and decreased in the 3.0 (2.64 ± 0.25 to 2.16 ± 0.33, P = .02) mU/kg/minute groups. Experiment 3: compared with baseline, MBFR increase was only borderline significant in metabolic syndrome and T2DM participants (1.98 ± 0.33 to 2.59 ± 0.45, P = .04, and 1.67 ± 0.35 to 2.14 ± 0.21, P = .05). Experiment 4: baseline percentage contrast defect length was similar in both groups but with insulin decreased with time and was significantly lower than in controls at 60 minutes (2.8 ± 5.7 vs 13.7 ± 10.6, P = .02). CONCLUSIONS: Presence of T2DM, insulin infusion duration, and dose are important determinants of the MBFR response to HE. When given immediately following revascularization for STEMI, insulin-dextrose reduces perfusion defect size at one hour. Hyperinsulinemic euglycemia may improve MBF following ischemia, but further studies are needed to clarify this.

M/M/Infinity Birth-Death Processes - A Quantitative Representational Framework to Summarize and Explain Phase Singularity and Wavelet Dynamics in Atrial Fibrillation.

RATIONALE: A quantitative framework to summarize and explain the quasi-stationary population dynamics of unstable phase singularities (PS) and wavelets in human atrial fibrillation (AF) is at present lacking. Building on recent evidence showing that the formation and destruction of PS and wavelets in AF can be represented as renewal processes, we sought to establish such a quantitative framework, which could also potentially provide insight into the mechanisms of spontaneous AF termination. OBJECTIVES: Here, we hypothesized that the observed number of PS or wavelets in AF could be governed by a common set of renewal rate constants λ f (for PS or wavelet formation) and λ d (PS or wavelet destruction), with steady-state population dynamics modeled as an M/M/∞ birth-death process. We further hypothesized that changes to the M/M/∞ birth-death matrix would explain spontaneous AF termination. METHODS AND RESULTS: AF was studied in in a multimodality, multispecies study in humans, animal experimental models (rats and sheep) and Ramirez-Nattel-Courtemanche model computer simulations. We demonstrated: (i) that λ f and λ d can be combined in a Markov M/M/∞ process to accurately model the observed average number and population distribution of PS and wavelets in all systems at different scales of mapping; and (ii) that slowing of the rate constants λ f and λ d is associated with slower mixing rates of the M/M/∞ birth-death matrix, providing an explanation for spontaneous AF termination. CONCLUSION: M/M/∞ birth-death processes provide an accurate quantitative representational architecture to characterize PS and wavelet population dynamics in AF, by providing governing equations to understand the regeneration of PS and wavelets during sustained AF, as well as providing insight into the mechanism of spontaneous AF termination.