Approximate probabilistic verification of hybrid systems

Hybrid systems whose mode dynamics are governed by non-linear ordinary differential equations (ODEs) are often a natural model for biological processes. However such models are difficult to analyze. To address this, we develop a probabilistic analysis method by approximating the mode transitions as stochastic events. We assume that the probability of making a mode transition is proportional to the measure of the set of pairs of time points and value states at which the mode transition is enabled. To ensure a sound mathematical basis, we impose a natural continuity property on the non-linear ODEs. We also assume that the states of the system are observed at discrete time points but that the mode transitions may take place at any time between two successive discrete time points. This leads to a discrete time Markov chain as a probabilistic approximation of the hybrid system. We then show that for BLTL (bounded linear time temporal logic) specifications the hybrid system meets a specification iff its Markov chain approximation meets the same specification with probability $1$. Based on this, we formulate a sequential hypothesis testing procedure for verifying -approximately- that the Markov chain meets a BLTL specification with high probability. Our case studies on cardiac cell dynamics and the circadian rhythm indicate that our scheme can be applied in a number of realistic settings

Real-world applicability and impact of early rhythm control for European patients with atrial fibrillation: a report from the ESC-EHRA EORP-AF Long-Term General Registry

Background: Use of rate/rhythm control is essential to control symptoms in patients with atrial fibrillation (AF). Recently, the EAST-AFNET 4 trial described how early rhythm control strategy was associated with a lower risk of adverse clinical outcomes. Objectives: The aim was to evaluate the real-world applicability and impact of an early rhythm control strategy in patients with AF. Methods: Use of an early rhythm control strategy was assessed in a European cohort of AF patients derived from the EHRA-ESC EORP-AF General Long-Term Registry. Early rhythm control was defined as use of antiarrhythmic drugs or cardioversion/catheter ablation. The primary outcome included cardiovascular death, stroke, acute coronary syndrome, and worsening of heart failure. Quality of life and health-care resource usage were also assessed as outcomes. Results: Among the 10,707 patients evaluated for eligibility to EAST-AFNET 4, a total of 3774 (34.0%) were included. Early rhythm control was associated with better quality of life, but with greater use of health-care resources. During follow-up, the primary outcome occurred less often in early rhythm control patients than in those with no rhythm control (13.6% vs. 18.5%, p < 0.001). In the multivariate adjusted Cox regression model, no significant difference was found between no rhythm control and early rhythm control, for the primary outcome. No difference in the primary outcome between early rhythm control and ‘no rhythm control patients’ adherent to Atrial fibrillation Better Care (ABC) pathway’ was evident (p = 0.753) Conclusions: Use of an early rhythm control strategy was associated with a lower rate of major adverse events, but this difference was non-significant on multivariate analysis, being mediated by differences in baseline characteristics and clinical risk profile. Early rhythm control was associated with a higher use of health-care resources and risk of hospital admission, despite showing better quality of life. Graphic abstract: [Figure not available: see fulltext.

Clinical complexity and impact of the ABC (Atrial fibrillation Better Care) pathway in patients with atrial fibrillation: a report from the ESC-EHRA EURObservational Research Programme in AF General Long-Term Registry

BACKGROUND: Clinical complexity is increasingly prevalent among patients with atrial fibrillation (AF). The 'Atrial fibrillation Better Care' (ABC) pathway approach has been proposed to streamline a more holistic and integrated approach to AF care; however, there are limited data on its usefulness among clinically complex patients. We aim to determine the impact of ABC pathway in a contemporary cohort of clinically complex AF patients. METHODS: From the ESC-EHRA EORP-AF General Long-Term Registry, we analysed clinically complex AF patients, defined as the presence of frailty, multimorbidity and/or polypharmacy. A K-medoids cluster analysis was performed to identify different groups of clinical complexity. The impact of an ABC-adherent approach on major outcomes was analysed through Cox-regression analyses and delay of event (DoE) analyses. RESULTS: Among 9966 AF patients included, 8289 (83.1%) were clinically complex. Adherence to the ABC pathway in the clinically complex group reduced the risk of all-cause death (adjusted HR [aHR]: 0.72, 95%CI 0.58-0.91), major adverse cardiovascular events (MACEs; aHR: 0.68, 95%CI 0.52-0.87) and composite outcome (aHR: 0.70, 95%CI: 0.58-0.85). Adherence to the ABC pathway was associated with a significant reduction in the risk of death (aHR: 0.74, 95%CI 0.56-0.98) and composite outcome (aHR: 0.76, 95%CI 0.60-0.96) also in the high-complexity cluster; similar trends were observed for MACEs. In DoE analyses, an ABC-adherent approach resulted in significant gains in event-free survival for all the outcomes investigated in clinically complex patients. Based on absolute risk reduction at 1 year of follow-up, the number needed to treat for ABC pathway adherence was 24 for all-cause death, 31 for MACEs and 20 for the composite outcome. CONCLUSIONS: An ABC-adherent approach reduces the risk of major outcomes in clinically complex AF patients. Ensuring adherence to the ABC pathway is essential to improve clinical outcomes among clinically complex AF patients

Primary care management for optimized antithrombotic treatment [PICANT]: study protocol for a cluster-randomized controlled trial

Background: Antithrombotic treatment is a continuous therapy that is often performed in general practice and requires careful safety management. The aim of this study is to investigate whether a best practice model that applies major elements of case management, including patient education, can improve antithrombotic management in primary health care in terms of reducing major thromboembolic and bleeding events. Methods: This 24-month cluster-randomized trial will be performed in 690 adult patients from 46 practices. The trial intervention will be a complex intervention involving general practitioners, health care assistants and patients with an indication for oral anticoagulation. To assess adherence to medication and symptoms in patients, as well as to detect complications early, health care assistants will be trained in case management and will use the Coagulation-Monitoring-List (Co-MoL) to regularly monitor patients. Patients will receive information (leaflets and a video), treatment monitoring via the Co-MoL and be motivated to perform self-management. Patients in the control group will continue to receive treatment-as-usual from their general practitioners. The primary endpoint is the combined endpoint of all thromboembolic events requiring hospitalization, and all major bleeding complications. Secondary endpoints are mortality, hospitalization, strokes, major bleeding and thromboembolic complications, severe treatment interactions, the number of adverse events, quality of anticoagulation, health-related quality of life and costs. Further secondary objectives will be investigated to explain the mechanism by which the intervention is effective: patients' assessment of chronic illness care, self-reported adherence to medication, general practitioners' and health care assistants' knowledge, patients' knowledge and satisfaction with shared decision making. Practice recruitment is expected to take place between July and December 2012. Recruitment of eligible patients will start in July 2012. Assessment will occur at three time points: baseline (T0), follow-up after 12 (T1) and after 24 months (T2). Discussion: The efficacy and effectiveness of individual elements of the intervention, such as antithrombotic interventions, self-management concepts in orally anticoagulated patients and the methodological tool, case-management, have already been extensively demonstrated. This project foresees the combination of several proven instruments, as a result of which we expect to profit from a reduction in the major complications associated with antithrombotic treatment

Factors Associated with Progression of Atrial Fibrillation and Impact on All-Cause Mortality in a Cohort of European Patients

Background: Paroxysmal atrial fibrillation (AF) may often progress towards more sustained forms of the arrhythmia, but further research is needed on the factors associated with this clinical course. Methods: We analyzed patients enrolled in a prospective cohort study of AF patients. Patients with paroxysmal AF at baseline or first-detected AF (with successful cardioversion) were included. According to rhythm status at 1 year, patients were stratified into: (i) No AF progression and (ii) AF progression. All-cause death was the primary outcome. Results: A total of 2688 patients were included (median age 67 years, interquartile range 60–75, females 44.7%). At 1-year of follow-up, 2094 (77.9%) patients showed no AF progression, while 594 (22.1%) developed persistent or permanent AF. On multivariable logistic regression analysis, no physical activity (odds ratio [OR] 1.35, 95% CI 1.02–1.78), valvular heart disease (OR 1.63, 95% CI 1.23–2.15), left atrial diameter (OR 1.03, 95% CI 1.01–1.05), or left ventricular ejection fraction (OR 0.98, 95% CI 0.97–1.00) were independently associated with AF progression at 1 year. After the assessment at 1 year, the patients were followed for an extended follow-up of 371 days, and those with AF progression were independently associated with a higher risk for all-cause death (adjusted hazard ratio 1.77, 95% CI 1.09–2.89) compared to no-AF-progression patients. Conclusions: In a contemporary cohort of AF patients, a substantial proportion of patients presenting with paroxysmal or first-detected AF showed progression of the AF pattern within 1 year, and clinical factors related to cardiac remodeling were associated with progression. AF progression was associated with an increased risk of all-cause mortality

The Registry of the German Competence NETwork on Atrial Fibrillation: patient characteristics and initial management

The aim of this study was to describe the characteristics of patients with atrial fibrillation (AF) enrolled in the Central Registry of the German Competence NETwork on Atrial Fibrillation (AFNET) and to assess current medical practice in patients treated at various levels of medical care in Germany. Methods From February 2004 to March 2006, 9582 ambulatory and hospitalized patients with ECG-documented AF were and results enrolled by 194 participating study centres from all levels of medical care in Germany. Clinical type of AF was reported as paroxysmal in 2893, persistent in 1873, and permanent in 3134 patients or classified as a first episode in 1035 patients. Predisposing conditions were common and present in 87.6 % of the patients. Most patients were symptomatic with AF (75.1%). Rhythm control in persistent AF was provided to 53.4 % of the symptomati

Local Control of Excitation-Contraction Coupling in Human Embryonic Stem Cell-Derived Cardiomyocytes

We investigated the mechanisms of excitation-contraction (EC) coupling in human embryonic stem cell-derived cardiomyocytes (hESC-CMs) and fetal ventricular myocytes (hFVMs) using patch-clamp electrophysiology and confocal microscopy. We tested the hypothesis that Ca2+ influx via voltage-gated L-type Ca2+ channels activates Ca2+ release from the sarcoplasmic reticulum (SR) via a local control mechanism in hESC-CMs and hFVMs. Field-stimulated, whole-cell [Ca2+]i transients in hESC-CMs required Ca2+ entry through L-type Ca2+ channels, as evidenced by the elimination of such transients by either removal of extracellular Ca2+ or treatment with diltiazem, an L-type channel inhibitor. Ca2+ release from the SR also contributes to the [Ca2+]i transient in these cells, as evidenced by studies with drugs interfering with either SR Ca2+ release (i.e. ryanodine and caffeine) or reuptake (i.e. thapsigargin and cyclopiazonic acid). As in adult ventricular myocytes, membrane depolarization evoked large L-type Ca2+ currents (ICa) and corresponding whole-cell [Ca2+]i transients in hESC-CMs and hFVMs, and the amplitude of both ICa and the [Ca2+]i transients were finely graded by the magnitude of the depolarization. hESC-CMs exhibit a decreasing EC coupling gain with depolarization to more positive test potentials, “tail” [Ca2+]i transients upon repolarization from extremely positive test potentials, and co-localized ryanodine and sarcolemmal L-type Ca2+ channels, all findings that are consistent with the local control hypothesis. Finally, we recorded Ca2+ sparks in hESC-CMs and hFVMs. Collectively, these data support a model in which tight, local control of SR Ca2+ release by the ICa during EC coupling develops early in human cardiomyocytes

Detection, Properties, and Frequency of Local Calcium Release from the Sarcoplasmic Reticulum in Teleost Cardiomyocytes

Calcium release from the sarcoplasmic reticulum (SR) plays a central role in the regulation of cardiac contraction and rhythm in mammals and humans but its role is controversial in teleosts. Since the zebrafish is an emerging model for studies of cardiovascular function and regeneration we here sought to determine if basic features of SR calcium release are phylogenetically conserved. Confocal calcium imaging was used to detect spontaneous calcium release (calcium sparks and waves) from the SR. Calcium sparks were detected in 16 of 38 trout atrial myocytes and 6 of 15 ventricular cells. The spark amplitude was 1.45±0.03 times the baseline fluorescence and the time to half maximal decay of sparks was 27±3 ms. Spark frequency was 0.88 sparks µm−1 min−1 while calcium waves were 8.5 times less frequent. Inhibition of SR calcium uptake reduced the calcium transient (F/F0) from 1.77±0.17 to 1.12±0.18 (p = 0.002) and abolished calcium sparks and waves. Moreover, elevation of extracellular calcium from 2 to 10 mM promoted early and delayed afterdepolarizations (from 0.6±0.3 min−1 to 8.1±2.0 min−1, p = 0.001), demonstrating the ability of SR calcium release to induce afterdepolarizations in the trout heart. Calcium sparks of similar width and duration were also observed in zebrafish ventricular myocytes. In conclusion, this is the first study to consistently report calcium sparks in teleosts and demonstrate that the basic features of calcium release through the ryanodine receptor are conserved, suggesting that teleost cardiac myocytes is a relevant model to study the functional impact of abnormal SR function

Reduced response to IKr blockade and altered hERG1a/1b stoichiometryin human heart failure

Heart failure (HF) claims 250,000 lives per year in the US, and nearly half of these deaths are sudden and presumably due to ventricular tachyarrhythmias. QT interval and action potential (AP) prolongation are hallmark proarrhythmic changes in the failing myocardium, which potentially result from alterations in repolarizing potassium currents. Thus,we aimed to examinewhether decreased expression of the rapid delayed rectifier potassiumcurrent, IKr, contributes to repolarization abnormalities in human HF. Tomap functional IKr expression across the left ventricle (LV), we optically imaged coronary-perfused LV free wall from donor and end-stage failing human hearts. The LV wedge preparation was used to examine transmural AP durations at 80% repolarization (APD80), and treatment with the IKr-blocking drug, E-4031, was utilized to interrogate functional expression. We assessed the percent change in APD80 post-IKr blockade relative to baseline APD80 (ΔAPD80) and found that ΔAPD80s are reduced in failing versus donor hearts in each transmural region, with 0.35-, 0.43-, and 0.41-fold reductions in endo-, mid-, and epicardium, respectively (p = 0.008, 0.037, and 0.022). We then assessed hERG1 isoform gene and protein expression levels using qPCR and Western blot. While we did not observe differences in hERG1a or hERG1b gene expression between donor and failing hearts, we found a shift in the hERG1a:hERG1b isoform stoichiometry at the protein level. Computer simulations were then conducted to assess IKr block under E-4031 influence in failing and nonfailing conditions. Our results confirmed the experimental observations and E-4031-induced relative APD80 prolongationwas greater in normal conditions than in failing conditions, provided that the cellularmodel of HF included a significant downregulation of IKr. In humanHF, the response to IKr blockade is reduced, suggesting decreased functional IKr expression. This attenuated functional response is associated with altered hERG1a:hERG1b protein stoichiometry in the failing human LV, and failing cardiomyoctye simulations support the experimental findings. Thus, of IKr protein and functional expression may be important determinants of repolarization remodeling in the failing human LV.We thank the Translational Cardiovascular Biobank & Repository (TCBR) at Washington University for provision of donor/patient records. The TCBR is supported by the NIH/CTSA (UL1 TR000448), Children's Discovery Institute, and Richard J. Wilkinson Trust. We also thank the laboratory of Dr. Sakiyama-Elbert for the use of the StepOnePlus equipment We appreciate the critical feedback on the manuscript by Dr. Jeanne Nerbonne. This work has been supported by the National Heart, Lung & Blood Institute (NHLBI, R01 HL114395). K. Holzem has been supported by the American Heart Association (12PRE12050315) and the NHLBI (F30 HL114310).Holzem, KM.; Gómez García, JF.; Glukhov, AV.; Madden, EJ.; Koppel, AC.; Ewald, GA.; Trénor Gomis, BA.... (2016). Reduced response to IKr blockade and altered hERG1a/1b stoichiometryin human heart failure. Journal of Molecular and Cellular Cardiology. 96:82-92. https://doi.org/10.1016/j.yjmcc.2015.06.008S82929

Simulation and Mechanistic Investigation of the Arrhythmogenic Role of the Late Sodium Current in Human Heart Failure

Heart failure constitutes a major public health problem worldwide. The electrophysiological remodeling of failing hearts sets the stage for malignant arrhythmias, in which the role of the late Na+ current (INaL) is relevant and is currently under investigation. In this study we examined the role of INaL in the electrophysiological phenotype of ventricular myocytes, and its proarrhythmic effects in the failing heart. A model for cellular heart failure was proposed using a modified version of Grandi et al. model for human ventricular action potential that incorporates the formulation of INaL. A sensitivity analysis of the model was performed and simulations of the pathological electrical activity of the cell were conducted. The proposed model for the human INaL and the electrophysiological remodeling of myocytes from failing hearts accurately reproduce experimental observations. The sensitivity analysis of the modulation of electrophysiological parameters of myocytes from failing hearts due to ion channels remodeling, revealed a role for INaL in the prolongation of action potential duration (APD), triangulation of the shape of the AP, and changes in Ca2+ transient. A mechanistic investigation of intracellular Na+ accumulation and APD shortening with increasing frequency of stimulation of failing myocytes revealed a role for the Na+/K+ pump, the Na+/Ca2+ exchanger and INaL. The results of the simulations also showed that in failing myocytes, the enhancement of INaL increased the reverse rate-dependent APD prolongation and the probability of initiating early afterdepolarizations. The electrophysiological remodeling of failing hearts and especially the enhancement of the INaL prolong APD and alter Ca2+ transient facilitating the development of early afterdepolarizations. An enhanced INaL appears to be an important contributor to the electrophysiological phenotype and to the dysregulation of [Ca2+]i homeostasis of failing myocytes