scholarly journals Directed Networks as a Novel Way to Describe and Analyze Cardiac Excitation: Directed Graph Mapping

2019 ◽  
Vol 10 ◽  
Author(s):  
Nele Vandersickel ◽  
Enid Van Nieuwenhuyse ◽  
Nico Van Cleemput ◽  
Jan Goedgebeur ◽  
Milad El Haddad ◽  
...  
Keyword(s):  
Directed Graph ◽  
Directed Networks ◽  
Graph Mapping ◽  
Cardiac Excitation

scholarly journals Directed networks as a novel way to describe and analyze cardiac excitation: Directed Graph mapping

2019 ◽  
Author(s):  
Nele Vandersickel ◽  
Enid Van Nieuwenhuyse ◽  
Nico Van Cleemput ◽  
Jan Goedgebeur ◽  
Milad El Haddad ◽  
...  
Keyword(s):  
Cardiac Arrhythmias ◽  
Normal Sinus Rhythm ◽  
Social Systems ◽  
Daily Practice ◽  
Directed Network ◽  
Directed Networks ◽  
Normal Sinus ◽  
Graph Mapping ◽  
Brain Data ◽  
Cardiac Excitation

AbstractNetworks provide a powerful methodology with applications in a variety of biological, technological and social systems such as analysis of brain data, social networks, internet search engine algorithms, etc. To date, directed networks have not yet been applied to characterize the excitation of the human heart. In clinical practice, cardiac excitation is recorded by multiple discrete electrodes. During (normal) sinus rhythm or during cardiac arrhythmias, successive excitation connects neighboring electrodes, resulting in their own unique directed network. This in theory makes it a perfect fit for directed network analysis. In this study, we applied directed networks to the heart in order to describe and characterize cardiac arrhythmias. Proofof-principle was established using in-silico and clinical data. We demonstrated that tools used in network theory analysis allow to determine the mechanism and location of certain cardiac arrhythmias. We show that the robustness of this approach can potentially exceed the existing state-of-the art methodology used in clinics. Furthermore, implementation of these techniques in daily practice can improve accuracy and speed of cardiac arrhythmia analysis. It may also provide novel insights in arrhythmias that are still incompletely understood.

scholarly journals Directed graph mapping is able to distinguish between the true and false rotors in a complex in-silico excitation pattern

EP Europace ◽  
2021 ◽  
Vol 23 (Supplement_3) ◽  
Author(s):  
E Van Nieuwenhuyse ◽  
L Martinez-Mateu ◽  
J Saiz ◽  
A V Panfilov ◽  
N Vandersickel
Keyword(s):  
Directed Graph ◽  
In Silico ◽  
Directed Network ◽  
Far Field ◽  
Field Effects ◽  
In Silico Studies ◽  
Basket Catheter ◽  
Graph Mapping ◽  
Excitation Pattern ◽  
Public Grant

Abstract Funding Acknowledgements Type of funding sources: Public grant(s) – EU funding. Main funding source(s): Supported in part by Dirección General de Polı́tica Cientı́fica de la Generalitat Valenciana PROMETEU 2020/043 Background In realistic in-silico studies (Figure1, top row) it was shown that phase mapping PM (Figure 1, A) can detect the correct rotor as well as phantom rotors as an artefact of interpolation or due to the far field (Figure 1, B). After interpretation of the LAT, the far field detections could not be distinguished from the true rotor driving the excitation pattern. This can contribute to failure in Atrial Fibrillation (AF) ablation procedures. Objective We tested if the recently developed tool Directed Graph mapping (DGM) is less prone to far-field effects and interpolation artefacts than PM on the same in-silico data. DGM represents the excitation pattern as a directed network, from which the rotational activity is detected as cycles in that network. Methods Starting from the electrograms (EGMs) of the 64 electrode basket catheter, we interpolated to 957 equidistant electrodes and calculated local activation times (LATs) of the interpolated EGMs (Figure 1, C). We varied the minimal allowed conduction velocity and calculated the corresponding networks for the complete simulation time. Detections were considered as correct if they were located in the same region of the true core of the phasemaps. The false detections were classified in multiple different regions (Figure 1, D). Results We find that by proper choice of CVs in the graphs it is possible to achieve a 80% detection of true rotors with 26% detection of false rotors. Reducing restrictions on the CVs increased the detection rate of the false rotors. False rotors due to artifacts were not detected by DGM (Figure 1, last row). Conclusion DGM is able to distinguish between true and far field rotors. False detections due to interpolation artifacts as seen in the PM protocol were not observed. The velocity limits in the graph construction play a keyrole in eliminating the far field effects. Abstract Figure 1

Weighted and Directed Graph Approaches

2018 ◽  
pp. 116-136
Keyword(s):  
Social Networks ◽  
Directed Graph ◽  
Shortest Path ◽  
Directed Networks ◽  
Multiple Paths ◽  
The Relationship ◽  
Linear Property

It is interesting to look at the types of social networks that are directed or weighted, or social networks with the combination of both. In many cases, the relationship between vertices may be quantifiable (weighted) or asymmetrical (directed). In this chapter, the authors first introduce the concept of weighted social networks and present an anonymization algorithm for these networks called the anonymity generalization algorithm. After that, they discuss k-anonymous path privacy and introduce the MSP algorithm. Next, the authors introduce the (k1, k2)-shortest path privacy and a (k1, k2)-shortest path privacy algorithm. Then they introduce directed weighted social networks and present the k-multiple paths anonymization on PV+NV (KMPPN). Also, the authors present a technique to convert directed networks into undirected networks. Finally, the authors present the linear property preserving anonymization approach for social networks.

Necessary and Sufficient Conditions for Group Consensus of Agents With Third-Order Dynamics in Directed Networks

2020 ◽  
Vol 142 (4) ◽  
Author(s):  
Onur Cihan ◽  
Mehmet Akar
Keyword(s):  
Directed Graph ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Group Consensus ◽  
Directed Networks ◽  
Third Order ◽  
Systematic Method ◽  
Necessary And Sufficient ◽  
The Given ◽  
Theoretical Results

Abstract In this paper, we investigate the group consensus problem in directed networks where agents have third-order dynamics. Necessary and sufficient conditions on the controller parameters are obtained to ensure K-equilibria group consensus where K is determined by the structure of the directed graph. It is theoretically shown that, for an arbitrary directed graph, there exist controller parameters that satisfy the given conditions. A systematic method for choosing the controller parameters to guarantee group consensus is suggested and theoretical results are verified by numerical examples.

scholarly journals Evaluation of Directed Graph-Mapping in Complex Atrial Tachycardias

2021 ◽  
Author(s):  
Enid Van Nieuwenhuyse ◽  
Teresa Strisciuglio ◽  
Giuseppe Lorenzo ◽  
Milad El Haddad ◽  
Jan Goedgebeur ◽  
...  
Keyword(s):  
Directed Graph ◽  
Graph Mapping

Exponential Consensus in Directed Networks of Multi-Agents with Saturated Protocols

2016 ◽  
Vol 16 (02) ◽  
pp. 1650003
Author(s):  
QINGLING WANG ◽  
YUANDA WANG
Keyword(s):  
Lyapunov Function ◽  
Directed Graph ◽  
Spanning Tree ◽  
Directed Graphs ◽  
Consensus Problem ◽  
Directed Networks ◽  
Strongly Connected ◽  
Theoretical Results ◽  
Multi Agents

This paper addresses the exponential consensus problem of single-integrator agents with saturated protocols on directed graphs. By employing an integral Lyapunov function, the exponential consensus problem of single-integrator agents is solved under the directed graph with strongly connected or a spanning tree. The main contribution is that under the directed graph, some conditions for exponential consensus with saturated protocols are first obtained. Finally, two examples are used to illustrate the effectiveness of the theoretical results.

scholarly journals Shortest Directed Networks in the Plane

2020 ◽  
Vol 36 (5) ◽  
pp. 1457-1475
Author(s):  
Alastair Maxwell ◽  
Konrad J. Swanepoel
Keyword(s):  
Directed Graph ◽  
Local Structure ◽  
Euclidean Plane ◽  
Directed Network ◽  
Directed Path ◽  
Directed Networks ◽  
Sources And Sinks ◽  
Steiner Points ◽  
Unpublished Work ◽  
The Given

Abstract Given a set of sources and a set of sinks as points in the Euclidean plane, a directed network is a directed graph drawn in the plane with a directed path from each source to each sink. Such a network may contain nodes other than the given sources and sinks, called Steiner points. We characterize the local structure of the Steiner points in all shortest-length directed networks in the Euclidean plane. This characterization implies that these networks are constructible by straightedge and compass. Our results build on unpublished work of Alfaro, Campbell, Sher, and Soto from 1989 and 1990. Part of the proof is based on a new method that uses other norms in the plane. This approach gives more conceptual proofs of some of their results, and as a consequence, we also obtain results on shortest directed networks for these norms.

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