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A super stable tensegrity introduced by Connelly in 1982 is a globally rigid discrete structure made from stiff bars and struts connected by cables with tension. We introduce the super stability number of a multigraph as the maximum dimension that a multigraph can be realized as a super stable tensegrity, and show that it equals the Colin de Verdière number ν $\nu $ minus one. As a corollary we obtain a combinatorial characterization of multigraphs that can be realized as three‐dimensional super stable tensegrities. We also show that, for any fixed d $d$, there is an infinite family of 3‐regular graphs that can be realized as d $d$‐dimensional injective super stable tensegrities. [ABSTRACT FROM AUTHOR]

Let D=(V+s,A) be a digraph with a designated root vertex s. Edmonds' seminal result (see J. Edmonds [4]) implies that D has a packing of k spanning s‐arborescences if and only if D has a packing of k(s,t)‐paths for all t∈V, where a packing means arc‐disjoint subgraphs. Let M be a matroid on the set of arcs leaving s. A packing of (s,t)‐paths is called M‐based if their arcs leaving s form a base of M while a packing of s‐arborescences is called M‐based if, for all t∈V, the packing of (s,t)‐paths provided by the arborescences is M‐based. Durand de Gevigney, Nguyen, and Szigeti proved in [3] that D has an M‐based packing of s‐arborescences if and only if D has an M‐based packing of (s,t)‐paths for all t∈V. Bérczi and Frank conjectured that this statement can be strengthened in the sense of Edmonds' theorem such that each s‐arborescence is required to be spanning. Specifically, they conjectured that D has an M‐based packing of spanning s‐arborescences if and only if D has an M‐based packing of (s,t)‐paths for all t∈V. In this paper we disprove this conjecture in its general form and we prove that the corresponding decision problem is NP‐complete. We also prove that the conjecture holds for several fundamental classes of matroids, such as graphic matroids and transversal matroids. For all the results presented in this paper, the undirected counterpart also holds. [ABSTRACT FROM AUTHOR]

Abstract: We present the case of a patient who developed regular, narrow QRS tachycardia after ablation for long-standing persistent atrial fibrillation. During the electrophysiological study, this tachycardia was diagnosed as macroreentrant atrial tachycardia circulating around the mitral annulus. Catheter ablation was performed to treat the tachycardia by targeting the linear region between the annulus and the left inferior pulmonary vein. Although linear radiofrequency application along the mitral isthmus (MI) line resulted in the termination of this tachycardia, a unidirectional conduction block was observed through the MI. Bidirectional conduction block was subsequently achieved by delivering supplemental radiofrequency energies at the gap on the MI. [Copyright &y& Elsevier]

PV and Linear Ablation for CFAEs. Introduction: Linear ablations in the left atrium (LA), in addition to pulmonary vein (PV) isolation, have been demonstrated to be an effective ablation strategy in patients with persistent atrial fibrillation (PsAF). This study investigated the impact of LA linear ablation on the complex-fractionated atrial electrograms (CFAEs) of PsAF patients. Methods and Results: A total of 40 consecutive PsAF patients (age: 54 ± 10 years, 39 males) who underwent catheter ablation were enrolled in this study. Linear ablation of both roofline between the right and left superior PVs and the mitral isthmus line joining from the mitral annulus to the left inferior PV were performed following PV isolation during AF. High-density automated CFAE mapping was performed using the NAVX, and maps were obtained 3 times during the procedure (prior to ablation, after PV isolation, and after linear ablations) and were compared. PsAF was terminated by ablation in 13 of 40 patients. The mean total LA surface area and baseline CFAEs area were 120.8 ± 23.6 and 88.0 ± 23.5 cm2 (74.2%), respectively. After PV isolation and linear ablations in the LA, the area of CFAEs area was reduced to 71.6 ± 22.6 cm2 (58.7%) (P < 0.001) and 44.9 ± 23.0 cm2 (39.2%) (P < 0.001), respectively. The LA linear ablations resulted in a significant reduction of the CFAEs area percentage in the region remote from ablation sites (from 56.3 ± 20.6 cm2 (59.6%) to 40.4 ± 16.5 cm2 (42.9%), P < 0.0001). Conclusion: Both PV isolation and LA linear ablations diminished the CFAEs in PsAF patients, suggesting substrate modification by PV and linear ablations. (J Cardiovasc Electrophysiol, Vol. 23, pp. 962-970, September 2012) [ABSTRACT FROM AUTHOR]

Peri-mitral atrial flutter, which is a type of macroreentrant atrial tachycardia circulating around the mitral annulus, was terminated with the guidance of the high-density mapping catheter. A 72-year-old woman with atrial fibrillation and atrial tachycardia presented with symptoms of congestive heart failure. The recurrent peri-mitral atrial flutter following the initial catheter ablation for atrial tachycardia and atrial fibrillation was terminated by radiofrequency application on the gap that was identified using a novel high-density mapping catheter. (PACE 2010; 1-4) [ABSTRACT FROM AUTHOR]

Background: Paroxysmal atrial fibrillation (PAF) can be treated with pulmonary vein isolation (PVI). A spectral analysis can identify sites of high-frequency activity during atrial fibrillation (AF). We investigated the role of the PVs on AF perpetuation by dominant frequency (DF) analysis. Methods: Thirty-one consecutive patients with PAF who underwent PVI were included in the prospective study. DF was calculated in each of the PVs, 16, five, and five sites in the left atrium, the coronary sinus, and the right atrium, respectively. In patients presenting sinus rhythm at the baseline, AF was induced by pacing. The PVs were then divided into two groups; PVs demonstrated the highest DF (HDF-PV) and others. Results: One patient was excluded from the analysis because sustained AF could not be induced. AF was terminated in 43.3% (13/30) of patients during ablation. Of 92 PVs isolated during AF, 30 and 62 PVs were classified into the HDF-PV and others, respectively. PAF was more frequently terminated by the HDF-PV isolation compared to the others (33.3%[10/30] vs 4.8%[3/62], P = 0.0004). Interestingly, nine of the 30 HDF-PVs showing the highest DF among all 30 regions, including extra PVs, led to AF termination in 88.9% (eight out of nine) of cases. Moreover, the HDF-PVs isolation resulted in a greater AF cycle length prolongation than the other PVs isolation (12.1±5.0 vs 2.7±7.6 ms, P = 0.007). Conclusion: Termination of PAF was more frequently observed during ablation of the PVs with the highest DF. The PV showing high DF played an important role in the maintenance of PAF. (PACE 2012; 35:28-37) [ABSTRACT FROM AUTHOR]

Completion of Mitral Isthmus Ablation. Background: Although mitral isthmus (MI) ablation in atrial fibrillation (AF) patients has been shown to be an effective ablative strategy, the establishment of the bidirectional conduction block of the MI is technically challenging. We investigated the usefulness of a steerable sheath for MI ablation in patients with persistent AF and its impact on the clinical outcome of persistent AF ablation. Methods: A total of 80 consecutive patients undergoing MI ablation were randomized to 1 of the following 2 groups: group S (using a steerable long sheath) or group NS (using a nonsteerable long sheath). MI ablation was performed by using an open-irrigated ablation catheter with the guidance of a 3-dimensional mapping system. The endpoint of the MI ablation was the achievement of a bidirectional block. Results: Bidirectional block through the MI was achieved in 87.5% (70/80) of patients with 14.0 ± 6.7 minutes of radiofrequency application. The bidirectional block was more frequently achieved in patients in group S compared to group NS (97.5% (39/40) vs 77.5% (31/40), P = 0.02). Additionally, epicardial ablation within the coronary sinus was less frequently required in group S compared to group NS (12.5% (5/40) vs 72.5% (29/40), P < 0.0001). Atrial tachycardia after the procedure more frequently occurred in the patients in whom MI block had not been achieved during the initial procedure (40.0% (4/10) vs 10.0% (7/70), P = 0.04). Conclusions: The MI block could be achieved in the majority of patients by using a steerable sheath. An incomplete MI block increased the risk of AT following persistent AF ablation. (J Cardiovasc Electrophysiol, Vol. 22, pp. 1331-1338, December 2011) [ABSTRACT FROM AUTHOR]

The article presents a case study of a 62 year old male patient who was hospitalized for persistent atrial fibrillation and congestive heart failure and underwent mitral isthmus catheter ablation for his atrial fibrillation. A discussion of echocardiograms which were conducted on the patient, and of the challenges that are involved with mitral isthmus ablation, is presented.

The article presents a case study of a 48 year old male who had recurrent atrial arrhythmia following catheter ablation of atrial fibrillation and was hospitalized as a result of his arrhythmia. A discussion of diagnostic testing which was conducted on the patient to investigate the arrhythmia, and of medical treatment which the patient received, is presented.