Optimal Timer Based Selection Schemes

Timer-based mechanisms are often used to help a given (sink) node select the best helper node among many available nodes. Specifically, a node transmits a packet when its timer expires, and the timer value is a monotone non-increasing function of its local suitability metric. The best node is selected successfully if no other node's timer expires within a 'vulnerability' window after its timer expiry, and so long as the sink can hear the available nodes. In this paper, we show that the optimal metric-to-timer mapping that (i) maximizes the probability of success or (ii) minimizes the average selection time subject to a minimum constraint on the probability of success, maps the metric into a set of discrete timer values. We specify, in closed-form, the optimal scheme as a function of the maximum selection duration, the vulnerability window, and the number of nodes. An asymptotic characterization of the optimal scheme turns out to be elegant and insightful. For any probability distribution function of the metric, the optimal scheme is scalable, distributed, and performs much better than the popular inverse metric timer mapping. It even compares favorably with splitting-based selection, when the latter's feedback overhead is accounted for.Comment: 21 pages, 6 figures, 1 table, submitted to IEEE Transactions on Communications, uses stackrel.st

Large deviations of the maximal eigenvalue of random matrices

We present detailed computations of the 'at least finite' terms (three dominant orders) of the free energy in a one-cut matrix model with a hard edge a, in beta-ensembles, with any polynomial potential. beta is a positive number, so not restricted to the standard values beta = 1 (hermitian matrices), beta = 1/2 (symmetric matrices), beta = 2 (quaternionic self-dual matrices). This model allows to study the statistic of the maximum eigenvalue of random matrices. We compute the large deviation function to the left of the expected maximum. We specialize our results to the gaussian beta-ensembles and check them numerically. Our method is based on general results and procedures already developed in the literature to solve the Pastur equations (also called "loop equations"). It allows to compute the left tail of the analog of Tracy-Widom laws for any beta, including the constant term.Comment: 62 pages, 4 figures, pdflatex ; v2 bibliography corrected ; v3 typos corrected and preprint added ; v4 few more numbers adde

Evaluation of Ablation Patterns Using a Biophysical Model of Atrial Fibrillation

Atrial fibrillation (AF) is the most common form of cardiac arrhythmia. Surgical/Radiofrequency (RF) ablation is a therapeutic procedure that consists of creating lines of conduction block to interrupt AF. The present study evaluated 13 different ablation patterns by means of a biophysical model of the human atria. In this model, ablation lines were abruptly applied transmurally during simulated sustained AF, and success rate, time to AF termination and average beat-to-beat interval were documented. The gold standard Cox's Maze III procedure was taken as reference. The effectiveness of twelve less invasive patterns was compared to it. In some of these incomplete lines (entailing a gap) were simulated. Finally, the computer simulations were compared to clinical data. The results show that the model reproduces observations made in vivo: (1) the Maze III is the most efficient ablation procedure; (2) less invasive patterns should include lines in both right and left atrium; (3) incomplete ablation lines between the pulmonary veins and the mitral valve annulus lead to uncommon flutter; (4) computer simulations of incomplete lines are consistent with clinical results of non-transumural RF ablation. Biophysical modeling may therefore be considered as a useful tool for understanding the mechanisms underlying AF therapie

Use of a biophysical model of atrial fibrillation in the interpretation of the outcome of surgical ablation procedures

OBJECTIVE: To determine the adequacy of 'in silico' biophysical models of atrial fibrillation (AF) in the design of different ablation line patterns. BACKGROUND: Permanent AF is a severe medical problem for which (surgical) ablation is a possible treatment. The ideal ablation pattern remains to be defined. METHODS: Forty-six consecutive adult patients with symptomatic permanent drug refractory AF underwent mitral surgery combined with non-transmural, (n=20) and transmural (n=26) radiofrequency Minimaze. The fraction of 'in vivo' conversions to sinus rhythm (SR) in both groups was compared with the performance of the fraction of 'in silico' conversions observed in a biophysical model of permanent AF. The simulations allowed us to study the effectiveness of incomplete and complete ablation patterns. A simulated, complete, transmural Maze III ablation pattern was applied to 118 different episodes of simulated AF set-up in the model and its effectiveness was compared with the clinical results reported by Cox. RESULTS: The fraction of conversions to SR was 92% 'in vivo' and 88% 'in silico' (p=ns) for transmural/complete ablations, 60% respectively 65% for non-transmural/incomplete Minimaze (p=ns) and 98% respectively 100% for Maze III ablations (p=ns). The fraction of conversions to SR 'in silico' correlated with the rates 'in vivo' (r2=0.973). CONCLUSIONS: The fraction of conversions to SR observed in the model closely corresponded to the conversion rate to SR post-surgery. This suggests that the model provides an additional, non-invasive tool for optimizing ablation line patterns for treating permanent AF

A biophysical model of atrial fibrillation to define the appropriate ablation pattern in modified maze

OBJECTIVE: The surgical Maze III procedure remains the gold standard in treating atrial fibrillation (AF); however due to clinical difficulties and higher risks, less invasive ablation alternatives are clinically investigated. The present study aims to define more efficient ablation patterns of the modified maze procedure using a biophysical model of human atria with chronic AF. METHODS: A three-dimensional model of human atria was developed using both MRI-imaging and a one-layer cellular model reproducing experimentally observed atrial cellular properties. Sustained AF could be induced by a burst-pacing protocol. Ablation lines were implemented in rendering the cardiac cells non-conductive, mimicking transmural lines. Lines were progressively implemented respectively around pulmonary veins (PV), left atrial appendage (LAA), left atrial isthmus (LAI), cavo-tricuspid isthmus (CTI), and intercaval lines (SIVC) in the computer model, defining the following patterns: P1=PV, P2=P1+LAA, P3=P2+LAI, P4=P3+CTI, P5=P3+SIVC, P6=P5+CTI. Forty simulations were done for each pattern and proportion of sinus rhythm (SR) conversion and time-to-AF termination (TAFT) were assessed. RESULTS: The most efficient patterns are P5, P6, and Maze III with 100% success. The main difference is expressed in decreasing mean TAFT with a correlation coefficient R=-0.8. There is an inflexion point for 100% success rate at a 7.5s TAFT, meaning that no additional line is mandatory beyond pattern P5. CONCLUSIONS: Our biophysical model suggests that Maze III could be simplified in his right atrial pattern to a single line joining both vena cavae. This has to be confirmed in clinical settings

EphA2-receptor deficiency exacerbates myocardial infarction and reduces survival in hyperglycemic mice

Background We have previously shown that EphrinA1/EphA expression profile changes in response to myocardial infarction (MI), exogenous EphrinA1-Fc administration following MI positively influences wound healing, and that deletion of the EphA2 Receptor (EphA2-R) exacerbates injury and remodeling. To determine whether or not ephrinA1-Fc would be of therapeutic value in the hyperglycemic infarcted heart, it is critical to evaluate how ephrinA1/EphA signaling changes in the hyperglycemic myocardium in response to MI. Methods Streptozotocin (STZ)-induced hyperglycemia in wild type (WT) and EphA2-receptor mutant (EphA2-R-M) mice was initiated by an intraperitoneal injection of STZ (150 mg/kg) 10 days before surgery. MI was induced by permanent ligation of the left anterior descending coronary artery and analyses were performed at 4 days post-MI. ANOVAs with Student-Newman Keuls multiple comparison post-hoc analysis illustrated which groups were significantly different, with significance of at least p < 0.05. Results Both WT and EphA2-R-M mice responded adversely to STZ, but only hyperglycemic EphA2-R-M mice had lower ejection fraction (EF) and fractional shortening (FS). At 4 days post-MI, we observed greater post-MI mortality in EphA2-R-M mice compared with WT and this was greater still in the EphA2-R-M hyperglycemic mice. Although infarct size was greater in hyperglycemic WT mice vs normoglycemic mice, there was no difference between hyperglycemic EphA2-R-M mice and normoglycemic EphA2-R-M mice. The hypertrophic response that normally occurs in viable myocardium remote to the infarct was noticeably absent in epicardial cardiomyocytes and cardiac dysfunction worsened in hyperglycemic EphA2-R-M hearts post-MI. The characteristic interstitial fibrotic response in the compensating myocardium remote to the infarct also did not occur in hyperglycemic EphA2-R-M mouse hearts to the same extent as that observed in the hyperglycemic WT mouse hearts. Differences in neutrophil and pan-leukocyte infiltration and serum cytokines implicate EphA2-R in modulation of injury and the differences in ephrinA1 and EphA6-R expression in governing this are discussed. Conclusions We conclude that EphA2-mutant mice are more prone to hyperglycemia-induced increased injury, decreased survival, and worsened LV remodeling due to impaired wound healing

Association between urinary biomarkers of total sugars intake and measures of obesity in a cross-sectional study

Obesity is an important modifiable risk factor for chronic diseases. While there is increasing focus on the role of dietary sugars, there remains a paucity of data establishing the association between sugar intake and obesity in the general public. The objective of this study was to investigate associations of estimated sugar intake with odds for obesity in a representative sample of English adults. We used data from 434 participants of the 2005 Health Survey of England. Biomarkers for total sugar intake were measured in 24 h urine samples and used to estimate intake. Linear and logistic regression analyses were used to investigate associations between biomarker-based estimated intake and measures of obesity (body mass intake (BMI), waist circumference and waist-to-hip ratio) and obesity risk, respectively. Estimated sugar intake was significantly associated with BMI, waist circumference and waist-to-hip ratio; these associations remained significant after adjustment for estimated protein intake as a marker of non-sugar energy intake. Estimated sugar intake was also associated with increased odds for obesity based on BMI (OR 1.02; 95%CI 1.00-1.04 per 10g), waist-circumference (1.03; 1.01-1.05) and waist-to-hip ratio (1.04; 1.02-1.06); all OR estimates remained significant after adjusting for estimated protein intake. Our results strongly support positive associations between total sugar intake, measures of obesity and likelihood of being obese. It is the first time that such an association has been shown in a nationally-representative sample of the general population using a validated biomarker. This biomarker could be used to monitor the efficacy of public health interventions to reduce sugar intake

Accuracy of popular automatic QT Interval algorithms assessed by a 'Gold Standard' and comparison with a Novel method: computer simulation study

BACKGROUND: Accurate measurement of the QT interval is very important from a clinical and pharmaceutical drug safety screening perspective. Expert manual measurement is both imprecise and imperfectly reproducible, yet it is used as the reference standard to assess the accuracy of current automatic computer algorithms, which thus produce reproducible but incorrect measurements of the QT interval. There is a scientific imperative to evaluate the most commonly used algorithms with an accurate and objective 'gold standard' and investigate novel automatic algorithms if the commonly used algorithms are found to be deficient. METHODS: This study uses a validated computer simulation of 8 different noise contaminated ECG waveforms (with known QT intervals of 461 and 495 ms), generated from a cell array using Luo-Rudy membrane kinetics and the Crank-Nicholson method, as a reference standard to assess the accuracy of commonly used QT measurement algorithms. Each ECG contaminated with 39 mixtures of noise at 3 levels of intensity was first filtered then subjected to three threshold methods (T1, T2, T3), two T wave slope methods (S1, S2) and a Novel method. The reproducibility and accuracy of each algorithm was compared for each ECG. RESULTS: The coefficient of variation for methods T1, T2, T3, S1, S2 and Novel were 0.36, 0.23, 1.9, 0.93, 0.92 and 0.62 respectively. For ECGs of real QT interval 461 ms the methods T1, T2, T3, S1, S2 and Novel calculated the mean QT intervals(standard deviations) to be 379.4(1.29), 368.5(0.8), 401.3(8.4), 358.9(4.8), 381.5(4.6) and 464(4.9) ms respectively. For ECGs of real QT interval 495 ms the methods T1, T2, T3, S1, S2 and Novel calculated the mean QT intervals(standard deviations) to be 396.9(1.7), 387.2(0.97), 424.9(8.7), 386.7(2.2), 396.8(2.8) and 493(0.97) ms respectively. These results showed significant differences between means at >95% confidence level. Shifting ECG baselines caused large errors of QT interval with T1 and T2 but no error with Novel. CONCLUSION: The algorithms T2, T1 and Novel gave low coefficients of variation for QT measurement. The Novel technique gave the most accurate measurement of QT interval, T3 (a differential threshold method) was the next most accurate by a large margin. The objective and accurate 'gold standard' presented in this paper may be useful to assess new QT measurement algorithms. The Novel algorithm may prove to be more accurate and reliable method to measure the QT interval

Atrial Heterogeneity Generates Re-entrant Substrate during Atrial Fibrillation and Anti-arrhythmic Drug Action: Mechanistic Insights from Canine Atrial Models

Anti-arrhythmic drug therapy is a frontline treatment for atrial fibrillation (AF), but its success rates are highly variable. This is due to incomplete understanding of the mechanisms of action of specific drugs on the atrial substrate at different stages of AF progression. We aimed to elucidate the role of cellular, tissue and organ level atrial heterogeneities in the generation of a re-entrant substrate during AF progression, and their modulation by the acute action of selected anti-arrhythmic drugs. To explore the complex cell-to-organ mechanisms, a detailed biophysical models of the entire 3D canine atria was developed. The model incorporated atrial geometry and fibre orientation from high-resolution micro-computed tomography, region-specific atrial cell electrophysiology and the effects of progressive AF-induced remodelling. The actions of multi-channel class III anti-arrhythmic agents vernakalant and amiodarone were introduced in the model by inhibiting appropriate ionic channel currents according to experimentally reported concentration-response relationships. AF was initiated by applied ectopic pacing in the pulmonary veins, which led to the generation of localized sustained re-entrant waves (rotors), followed by progressive wave breakdown and rotor multiplication in both atria. The simulated AF scenarios were in agreement with observations in canine models and patients. The 3D atrial simulations revealed that a re-entrant substrate was typically provided by tissue regions of high heterogeneity of action potential duration (APD). Amiodarone increased atrial APD and reduced APD heterogeneity and was more effective in terminating AF than vernakalant, which increased both APD and APD dispersion. In summary, the initiation and sustenance of rotors in AF is linked to atrial APD heterogeneity and APD reduction due to progressive remodelling. Our results suggest that anti-arrhythmic strategies that increase atrial APD without increasing its dispersion are effective in terminating AF

MRI roadmap-guided transendocardial delivery of exon-skipping recombinant adeno-associated virus restores dystrophin expression in a canine model of Duchenne muscular dystrophy

Duchenne muscular dystrophy (DMD) cardiomyopathy patients currently have no therapeutic options. We evaluated catheter-based transendocardial delivery of a recombinant adeno-associated virus (rAAV) expressing a small nuclear U7 RNA (U7smOPT) complementary to specific cis-acting splicing signals. Eliminating specific exons restores the open-reading frame resulting in translation of truncated dystrophin protein. To test this approach in a clinically relevant DMD model, golden retriever muscular dystrophy (GRMD) dogs received serotype 6 rAAV-U7smOPT via the intracoronary or transendocardial route. Transendocardial injections were performed with an injection-tipped catheter and fluoroscopic guidance using X-ray fused with MRI (XFM) roadmaps. Three months after treatment, tissues were analyzed for DNA, RNA, dystrophin protein, and histology. Whereas intracoronary delivery did not result in effective transduction, transendocardial injections, XFM guidance, enabled 30±10 non-overlapping injections per animal. Vector DNA was detectable in all samples tested and ranged from 3000 vector genome copies per cell. RNA analysis, western blot analysis, and immunohistology demonstrated extensive expression of skipped RNA and dystrophin protein in the treated myocardium. Left ventricular function remained unchanged over a three-month follow-up. These results demonstrated that effective transendocardial delivery of rAAV-U7smOPT was achieved using XFM. This approach restores an open reading frame for dystrophin in affected dogs and has potential clinical utility