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1. Cilium and VDM -- Towards Formal Analysis of Cilium Policies

Author

Kulik, Tomas and Boudjadar, Jalil

Subjects
Computer Science - Distributed, Parallel, and Cluster Computing, Computer Science - Software Engineering
Abstract

Industrial control systems are becoming more distributed and interconnected to allow for interaction with modern computing infrastructures. Furthermore, the amount of data generated by these systems is increasing due to integration of more sensors and the need to increase the reliability of the system based on predictive data models. One challenge in accommodating this data and interconnectivity increase is the change of the architecture of these systems from monolithic to component based, distributed systems. Questions such as how to deploy and operate such distributed system with many sub-components arise. One approach is the use of kubernetes to orchestrate the different components as containers. The critical nature of the industrial control systems however often requires strict component isolation and network segmentation to satisfy security requirements. Cilium is a popular network overlay for kubernetes that enables definition of network policies between different components running as kubernetes pods. The network policies are crucial for maintaining the secure operation of the system, however analysis of deployed policies is often lacking. In this paper, we explore the use of a formal analysis of Cilium network policies using VDM-SL. We provide examples of Cilium policies, an approach how they could be formalised using VDM-SL and analyse several scenarios to validate the policies against a model of simple real-life system.

Published
2024

2. State of the Art Report: Verified Computation

Author

Woodcock, Jim, Andersen, Mikkel Schmidt, Aranha, Diego F., Hallerstede, Stefan, Hansen, Simon Thrane, Jakobsen, Nikolaj Kuhne, Kulik, Tomas, Larsen, Peter Gorm, Macedo, Hugo Daniel, Martin, Carlos Ignacio Isasa, and Norrild, Victor Alexander Mtsimbe

Subjects
Computer Science - Cryptography and Security
Abstract

This report describes the state of the art in verifiable computation. The problem being solved is the following: The Verifiable Computation Problem (Verifiable Computing Problem) Suppose we have two computing agents. The first agent is the verifier, and the second agent is the prover. The verifier wants the prover to perform a computation. The verifier sends a description of the computation to the prover. Once the prover has completed the task, the prover returns the output to the verifier. The output will contain proof. The verifier can use this proof to check if the prover computed the output correctly. The check is not required to verify the algorithm used in the computation. Instead, it is a check that the prover computed the output using the computation specified by the verifier. The effort required for the check should be much less than that required to perform the computation. This state-of-the-art report surveys 128 papers from the literature comprising more than 4,000 pages. Other papers and books were surveyed but were omitted. The papers surveyed were overwhelmingly mathematical. We have summarised the major concepts that form the foundations for verifiable computation. The report contains two main sections. The first, larger section covers the theoretical foundations for probabilistically checkable and zero-knowledge proofs. The second section contains a description of the current practice in verifiable computation. Two further reports will cover (i) military applications of verifiable computation and (ii) a collection of technical demonstrators. The first of these is intended to be read by those who want to know what applications are enabled by the current state of the art in verifiable computation. The second is for those who want to see practical tools and conduct experiments themselves., Comment: 54 pages

Published
2023

4. A Survey of Practical Formal Methods for Security

Author

Kulik, Tomas, Dongol, Brijesh, Larsen, Peter Gorm, Macedo, Hugo Daniel, Schneider, Steve, Tran-Jørgensen, Peter Würtz Vinther, and Woodcock, Jim

Subjects
Computer Science - Formal Languages and Automata Theory, Computer Science - Cryptography and Security
Abstract

In today's world, critical infrastructure is often controlled by computing systems. This introduces new risks for cyber attacks, which can compromise the security and disrupt the functionality of these systems. It is therefore necessary to build such systems with strong guarantees of resiliency against cyber attacks. One way to achieve this level of assurance is using formal verification, which provides proofs of system compliance with desired cyber security properties. The use of Formal Methods (FM) in aspects of cyber security and safety-critical systems are reviewed in this article. We split FM into the three main classes: theorem proving, model checking and lightweight FM. To allow the different uses of FM to be compared, we define a common set of terms. We further develop categories based on the type of computing system FM are applied in. Solutions in each class and category are presented, discussed, compared and summarised. We describe historical highlights and developments and present a state-of-the-art review in the area of FM in cyber security. This review is presented from the point of view of FM practitioners and researchers, commenting on the trends in each of the classes and categories. This is achieved by considering all types of FM, several types of security and safety critical systems and by structuring the taxonomy accordingly. The article hence provides a comprehensive overview of FM and techniques available to system designers of security-critical systems, simplifying the process of choosing the right tool for the task. The article concludes by summarising the discussion of the review, focusing on best practices, challenges, general future trends and directions of research within this field., Comment: Technical Report, Long survey version

Published
2021

5. Formal Model In-The-Loop for Secure Industrial Control Networks

Author

Ubys, Laurynas, Nicolas Vancea, Valeriu, Kulik, Tomas, Gorm Larsen, Peter, Boudjadar, Jalil, Aranha, Diego F., Goos, Gerhard, Founding Editor, Hartmanis, Juris, Founding Editor, Bertino, Elisa, Editorial Board Member, Gao, Wen, Editorial Board Member, Steffen, Bernhard, Editorial Board Member, Yung, Moti, Editorial Board Member, Tapia Tarifa, Silvia Lizeth, editor, and Proença, José, editor

Published
2022
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6. Towards Secure Digital Twins

Author

Kulik, Tomas, Gomes, Cláudio, Macedo, Hugo Daniel, Hallerstede, Stefan, Larsen, Peter Gorm, Goos, Gerhard, Founding Editor, Hartmanis, Juris, Founding Editor, Bertino, Elisa, Editorial Board Member, Gao, Wen, Editorial Board Member, Steffen, Bernhard, Editorial Board Member, Yung, Moti, Editorial Board Member, and Margaria, Tiziana, editor

Published
2022
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8. Formal Security Analysis of Cloud-Connected Industrial Control Systems

Author

Kulik, Tomas, Tran-Jørgensen, Peter W. V., Boudjadar, Jalil, Hutchison, David, Series Editor, Kanade, Takeo, Series Editor, Kittler, Josef, Series Editor, Kleinberg, Jon M., Series Editor, Mattern, Friedemann, Series Editor, Mitchell, John C., Series Editor, Naor, Moni, Series Editor, Pandu Rangan, C., Series Editor, Steffen, Bernhard, Series Editor, Terzopoulos, Demetri, Series Editor, Tygar, Doug, Series Editor, Lanet, Jean-Louis, editor, and Toma, Cristian, editor

Published
2019
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13. Randomized comparison of atrioventricular node re-entry tachycardia and atrial flutter catheter ablation with and without fluoroscopic guidance: ZeroFluoro study

Author

Lehar, Frantisek, primary, Szegedi, Nándor, additional, Hejc, Jakub, additional, Jez, Jiri, additional, Soucek, Filip, additional, Kulik, Tomas, additional, Siruckova, Anna, additional, Sallo, Zoltan, additional, Nagy, Klaudia Vivien, additional, Merkely, Bela, additional, Geller, László, additional, and Starek, Zdeněk, additional

Published
2022
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17. OPTIMZIED CT SCANNING PROTOCOL OF THE LEFT ATRIUM PRIOR TO RADIOFREQUENCY CATHETER ABLATION IN PATIENTS WITH ATRIAL FIBRILLATION

Author

Jadczyk, Tomasz, primary, Wolf, Jiri, additional, Pesl, Martin, additional, Soucek, Filip, additional, Lehar, František, additional, Jez, Jiri, additional, Kulik, Tomas, additional, Tyshchenko, Bohdan, additional, Belaskova, Silvie, additional, Ourednicek, Petr, additional, Caluori, Guido, additional, Novak, Miroslav, additional, and Starek, Zdenek, additional

Published
2022
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18. Reduced Radiation Exposure Protocol during Computer Tomography of the Left Atrium Prior to Catheter Ablation in Patients with Atrial Fibrillation

Author

Jadczyk, Tomasz, primary, Wolf, Jiri, additional, Pesl, Martin, additional, Soucek, Filip, additional, Lehar, Frantisek, additional, Jez, Jiri, additional, Kulik, Tomas, additional, Tyshchenko, Bohdan, additional, Belaskova, Silvie, additional, Ourednicek, Petr, additional, Caluori, Guido, additional, Novak, Miroslav, additional, and Starek, Zdenek, additional

Published
2022
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22. Formal Methods in Security Survey

Author

Kulik, Tomas, Dongol, Brijesh, Larsen, Peter Gorm, Macedo, Hugo Daniel, Schneider, Steve, Tran-Jørgensen, Peter Würtz Vinther, and Woodcock, Jim

Abstract

In today’s world, critical infrastructure is often controlled by computing systems. This introducesnew risks for cyber attacks, which can compromise the security and disrupt the functionality of these systems.It is therefore necessary to build such systems with strong guarantees of resiliency against cyber attacks.One way to achieve this level of assurance is using formal verification, which provides proofs of systemcompliance with desired cyber security properties. The use of Formal Methods (FM) in aspects of cybersecurity and safety-critical systems are reviewed in this article. We split FM into the three main classes:theorem proving, model checking and lightweight FM. To allow the different uses of FM to be compared,we define a common set of terms. We further develop categories based on the type of computing system FMare applied in. Solutions in each class and category are presented, discussed, compared and summarised.We describe historical highlights and developments and present a state-of-the-art review in the area of FMin cyber security. This review is presented from the point of view of FM practitioners and researchers,commenting on the trends in each of the classes and categories. This is achieved by considering all typesof FM, several types of security and safety critical systems and by structuring the taxonomy accordingly.The article hence provides a comprehensive overview of FM and techniques available to system designers ofsecurity-critical systems, simplifying the process of choosing the right tool for the task. The article concludesby summarising the discussion of the review, focusing on best practices, challenges, general future trendsand directions of research within this field.

Published
2020

23. Provable Cyber-Security for Industrial Control Systems

Author

Kulik, Tomas

Abstract

Kompleksiten af industrielle styresystemer (ISS) vokser sammen med deres forbindelser til andre systemer. Det er vigtigt at sådanne systemer er sikret mod potentiel cyber-angreb fordi et kompromitteret ISS ville føre til betydelig økonomisk skade eller tab af vigtig information. For at sikre disse systemers sikkerhed er det vigtigt at overveje cyber-sikkerheds principper allerede tidligt i systemets design. En måde at anlysere cyber-sikkerheden tidligt er ved anvendelse af formelle metoder, hvor en semantisk model af systemet vil kunne analyseres mod sikkerhedsegenskaber. Den primære teknik anvendt i denne afhandling bliver kaldt model checking. Formål et med dette er at tilvejebringe metoder og teknikker til formalisering og analyse af komplekse ISS’er samt kunne demonstrere hvordan det at følge en sikkerhedsstandard kan bestemmes i ISS-designstadiet. Det overordnede mål er at demonstrere at sådanne teknikker kan tilføje formelle sikkerhedsanalyser til det industrielle udviklingsværktøjssæt. Disse mål realiseres ved en række bidrag inden for formalisering af komplekse ISS arkitekturer, formalisering af cyber- sikkerhedsstandarder, levering af teknikker til at håndtere kompleksitet under formel analyse og ved at undersøge forskningsområdet for formelle metoder inden for sikkerhed. Disse bidrag har leveret indsigt, fremskridt og metoder til industriel anvendelighed af formelle metoder samt peget på yderligere forsknings behov. Industrial Control Systems (ICSs) are becoming increasingly complex and interconnected. It is important for these systems to be secure against potential cyber attacks, as a compromised ICS could lead to significant financial damages or loss of important information. In order to ensure the security of these systems it is important to consider cyber-security and potential attacks already early in the design stages of these systems. One way of doing this is by use of formal methods, where a semantic model of the system can be analyzed against a collection of cyber-security properties. The main approach used within this thesis is model checking with the aim to provide methods and techniques to formalization and analysis of complex ICSs as well as to demonstrate how a cyber-security standard compliance could be determined at the design stage of the ICS. The overall aim is to demonstrate such techniques to the industrial partner with the goal of adding the formal security analysis to the industrial development toolkit. This is realized by several contributions within the area of formalization of complex ICS architectures, formalization of aspects of cyber-security standards, providing techniques for dealing with complexity with formal analysis and surveying the research field of formal methods in security. These contributions have provided insights, advancements and methods for industrial applicability of formal methods as well as towards potential further research.

Published
2020

32. Three-dimensional rotational angiography of the left atrium and the oesophagus: the short-term mobility of the oesophagus and the stability of the fused three-dimensional model of the left atrium and the oesophagus during catheter ablation for atrial fibrillation

Author

Starek, Zdenek, primary, Lehar, Frantisek, additional, Jez, Jiri, additional, Scurek, Martin, additional, Wolf, Jiri, additional, Kulik, Tomas, additional, Zbankova, Alena, additional, and Novak, Miroslav, additional

Published
2016
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35. Comparison of clinical outcomes and safety of catheter ablation for atrial fibrillation supported by data from CT scan or three-dimensional rotational angiogram of left atrium and pulmonary veins

Author

Lehar, Frantisek, primary, Starek, Zdenek, additional, Jez, Jiri, additional, Novak, Miroslav, additional, Wolf, Jiri, additional, Stepanova, Radka, additional, Kruzliak, Peter, additional, Kulik, Tomas, additional, Zbankova, Alena, additional, Jancar, Radek, additional, and Vitovec, Jiri, additional

Published
2015
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36. Detailed analysis of the relationship between the left atrium and esophagus in patients prior to catheter ablation of atrial fibrillation: an analysis using 3D computed tomography.

Author

Starek, Zdenek, Lehar, Frantisek, Jez, Jiri, Wolf, Jiri, Kulik, Tomas, and Kulikova, Alena

Abstract

Background. Damage to the esophagus during radiofrequency ablation of atrial fibrillation can result in fatal atrioesophageal fistula. Our aim is to describe the relationship of the left atrium (LA) and esophagus with a focus on contact of the posterior wall (PW) of the LA and the esophagus. Methods. From 9/2011 to 8/2012, CT of the heart was performed in 56 patients undergoing catheter ablation of atrial fibrillation using CT GE Lightspeed VCT 64 by nongated standard protocol. Positions of the esophagus to the LA, width of the esophagus and contact with the PW of the LA were determined. Results. The most frequent position of the esophagus was behind the left side of the LA. The average width of the esophagus was 16.0 ± 4.1 mm, and the average distance between the PW and esophagus was 4.8 ± 1.6 mm. On average, 50 ± 4.11 mm of the PW was in close contact with the esophagus. The average length of the fat pad between the esophagus and LA was 9.1 ± 5.5 mm in the upper part of the LA and 15.8 ± 7.3 mm at the bottom. Significantly longer contact occurred behind the right part of the LA. Conclusions. The most common esophageal position is behind the left side of the LA. The esophagus is located in close contact by approximately 2/3 of the length and 1/4 of the width of the PW of the LA. The esophagus is more adjacent to the upper part of PW of the LA. [ABSTRACT FROM AUTHOR]

Published
2017

37. Feasibility and safety of right and left ventricular three-dimensional rotational angiography for guiding catheter ablation of ventricular arrhythmias.

Author

Starek, Zdenek, Wolf, Jiri, Lehar, Frantisek, Jez, Jiri, Kulik, Tomas, and Kulikova, Alena

Abstract

Background. Three-dimensional rotational angiography (3DRA) of the heart is an imaging technique that displays the left atrium and adjacent structures during catheter ablation of atrial fibrillation. The aim is to evaluate the feasibility and safety of 3DRA for imaging the right and left ventricles of patients undergoing catheter ablation of ventricular arrhythmias. Methods. From 8/2010 to 6/2015, 35 patients underwent 3DRA of the right (20 patients) or left ventricle (15 patients) with a Philips Allura FD 10 X-ray system using a direct protocol. The success rate of the 3D model, as well as the procedure times and complications of 3DRA, was evaluated, and the 3DRA model was compared with ventricular computer tomography (CT). Results. The overall 3D model success rate was 91.4%. The 3D models were graded as excellent for 65.7% of patients and as useful for 25.7% of patients. The imaging success rate was slightly higher for the right ventricle than for the left ventricle (95%, 86.7%, respectively). The times required to perform 3DRA of the right and left ventricle were 12.5 +/- 2.1 min and 14.7 +/- 2.8 min, respectively. There were no significant differences between 3DRA and ventricular CT. Conclusion. Ventricular 3DRA allows the easy and safe creation of 3D models of the cardiac ventricles. The success rate is comparable to the success rate of the 3DRA for imaging the left atrium. There was no difference in imaging quality between the two ventricles. 3DRA models of the ventricles are comparable with CT models of the ventricles. [ABSTRACT FROM AUTHOR]

Published
2017

38. Comparison of radiation exposure, contrast agent consumption and cost effectiveness between computer tomography and 3D rotational angiography of the left atrium to guide catheter ablation in patients with atrial fibrillation.

Author

Starek, Zdenek, Lehar, Frantisek, Jez, Jiri, Wolf, Jiri, Kulik, Tomas, and Kulikova, Alena

Abstract

Background. Catheter ablation of complex atrial arrhythmias guided by 3D models of a left atrium (LA) derived from CT/MRI or 3D rotational angiography of the heart (3DRA) is currently a common practice. Our aim is to compare radiation dose, consumption of a contrast agent and cost of these methods. Methods. From 10/2012 to 10/2015, either 3DRA (157 patients using the X-ray system Philips Allura FD 10) or computer tomography (CT) (157 patients using 64-slice CT GE Lightspeed VCT) of the LA was performed in patients undergoing complex atrial arrhythmias ablation. All procedures were monitored for average effective radiation dose, dose of the contrast agent and analysis of a financial expenditures. Results. The average effective radiation dose for 3DRA was 2.11±0.392 mSv compared to 10.52±2.093 mSv for CT. The contrast agent consumption was 22.2 mg and 48.2 mg of iodine for 3DRA and CT, respectively. Total price per procedure is 123€ for 3DRA and 161€ for CT. Conclusion. Consumption of the contrast agent and radiation burden for LA 3DRA is significantly lower in comparison to most currently used CT scan methods. Cost of both methods is comparable, however, 3DRA is slightly less expensive than CT. [ABSTRACT FROM AUTHOR]

Published
2017

39. Three-dimensional rotational angiography of the left atrium and the oesophagus: the short-term mobility of the oesophagus and the stability of the fused three-dimensional model of the left atrium and the oesophagus during catheter ablation for atrial fibrillation.

Author

Starek, Zdenek, Lehar, Frantisek, Jez, Jiri, Scurek, Martin, Wolf, Jiri, Kulik, Tomas, Zbankova, Alena, and Novak, Miroslav

Subjects
ANGIOGRAPHY, ATRIAL fibrillation, HUMAN body, CATHETER ablation, DIAGNOSTIC imaging, ESOPHAGUS, FLUOROSCOPY, HEART atrium, LONGITUDINAL method, COMPUTERS in medicine, MOTION, INTERVENTIONAL radiology, RESEARCH evaluation, TIME, THREE-dimensional imaging, TREATMENT effectiveness, PREDICTIVE tests, COMPUTER-assisted surgery, SURGERY
Abstract

Aims: The objective of this study was to evaluate the mobility of the oesophagus and the stability of the three-dimensional (3D) model of the oesophagus using 3D rotational angiography (3DRA) of the left atrium (LA) and the oesophagus, fused with live fluoroscopy during catheter ablation for atrial fibrillation.Methods and Results: From March 2015 to September 2015, 3DRA of the LA and the oesophagus was performed in 33 patients before catheter ablation for atrial fibrillation. Control contrast oesophagography was performed every 30 min. The positions of the oesophagograms and the 3D model of the LA and the oesophagus were repeatedly measured and compared with the spine. The average shift of the oesophagus ranged from 2.7 ± 2.2 to 5.0 ± 3.5 mm. The average real-time oesophageal shift ranged from 2.7 ± 2.2 to 3.8 ± 3.4 mm. No significant shift was detected until the 90th minute of the procedure. The average shift of the 3D model of the LA and the oesophagus ranged from 1.4 ± 1.8 to 3.3 ± 3.0 mm (right-left direction) and from 0.9 ± 1.2 to 2.2 ± 1.3 mm (craniocaudal direction). During the 2 h procedure, there were no significant shifts of the model.Conclusion: During catheter ablation for atrial fibrillation, there is no significant change in the position of the oesophagus until the 90th minute of the procedure and no significant shift in the 3D model of the LA and the oesophagus. The 3D model of the oesophagus reliably depicts the position of the oesophagus during the entire procedure. [ABSTRACT FROM AUTHOR]

Published
2017
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41. Randomized comparison of atrioventricular node re-entry tachycardia and atrial flutter catheter ablation with and without fluoroscopic guidance: ZeroFluoro study.

Author

Lehar F, Szegedi N, Hejc J, Jez J, Soucek F, Kulik T, Siruckova A, Sallo Z, Nagy KV, Merkely B, Geller L, and Starek Z

Subjects
Arrhythmias, Cardiac surgery, Atrioventricular Node, Fluoroscopy methods, Humans, Middle Aged, Prospective Studies, Treatment Outcome, Atrial Flutter diagnostic imaging, Atrial Flutter surgery, Catheter Ablation adverse effects, Catheter Ablation methods, Tachycardia, Atrioventricular Nodal Reentry diagnostic imaging, Tachycardia, Atrioventricular Nodal Reentry surgery, Tachycardia, Supraventricular diagnostic imaging, Tachycardia, Supraventricular surgery
Abstract

Aims: Interventional cardiology procedures may expose patients and staff to considerable radiation doses. We aimed to assess whether exposure to ionizing radiation during catheter ablation of supraventricular tachycardia (SVT) can be completely avoided., Methods and Results: In this prospective randomized study, patients with SVT (atrioventricular re-entrant tachycardia n = 94, typical atrial flutter n = 29) were randomly assigned in a 1:1 ratio to catheter ablation with conventional fluoroscopic guidance (CF group) or with the EnSite Precision mapping system [zerofluoro (ZF) group]. Acute procedural parameters, increased stochastic risk of cancer incidence and 6-month follow-up data were assessed. Between May 2019 and August 2020, 123 patients were enrolled. Clinical parameters were comparable. Median procedural time was 60.0 and 58.0 min, median fluoroscopy time and estimated median effective dose were 240 s vs. 0 and 0.38 mSv vs. 0 and arrhythmia recurrence was 5% and 7.9% in the CF and ZF groups, respectively. The acute success rate was 98.4% in both groups. No procedure-related complications were reported. At an average age of 55.5 years and median radiation exposure of 0.38 mSv, the estimate of increased incidence was approximately 1 in 14 084. The estimated mortality rate was 1 per 17 857 exposed persons., Conclusions: The procedural safety and efficacy of the zero-fluoroscopic approach are similar to those of conventional fluoroscopy-based ablation for atrioventricular nodal re-entrant tachycardia and atrial flutter. Under the assumption of low radiation dose, the excessive lifetime risk of malignancy in the CF group due to electrophysiology procedure is reasonably small, whilst totally reduced in zero fluoroscopy procedures., Competing Interests: Conflict of interest: N.S. and L.G. reports consulting fees from Abbott, not related to the present study., (© The Author(s) 2022. Published by Oxford University Press on behalf of European Society of Cardiology. All rights reserved. For permissions, please e-mail: journals.permissions@oup.com.)

Published
2022
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42. Three-dimensional rotational angiography of the left atrium and the oesophagus: the short-term mobility of the oesophagus and the stability of the fused three-dimensional model of the left atrium and the oesophagus during catheter ablation for atrial fibrillation.

Author

Starek Z, Lehar F, Jez J, Scurek M, Wolf J, Kulik T, Zbankova A, and Novak M

Subjects
Aged, Anatomic Landmarks, Atrial Fibrillation physiopathology, Catheter Ablation adverse effects, Female, Fluoroscopy, Heart Atria physiopathology, Humans, Male, Middle Aged, Motion, Operative Time, Predictive Value of Tests, Prospective Studies, Reproducibility of Results, Surgery, Computer-Assisted adverse effects, Time Factors, Treatment Outcome, Angiography methods, Atrial Fibrillation diagnostic imaging, Atrial Fibrillation surgery, Catheter Ablation methods, Esophagus diagnostic imaging, Heart Atria diagnostic imaging, Heart Atria surgery, Imaging, Three-Dimensional, Radiographic Image Interpretation, Computer-Assisted, Radiography, Interventional methods, Surgery, Computer-Assisted methods
Abstract

Aims: The objective of this study was to evaluate the mobility of the oesophagus and the stability of the three-dimensional (3D) model of the oesophagus using 3D rotational angiography (3DRA) of the left atrium (LA) and the oesophagus, fused with live fluoroscopy during catheter ablation for atrial fibrillation., Methods and Results: From March 2015 to September 2015, 3DRA of the LA and the oesophagus was performed in 33 patients before catheter ablation for atrial fibrillation. Control contrast oesophagography was performed every 30 min. The positions of the oesophagograms and the 3D model of the LA and the oesophagus were repeatedly measured and compared with the spine. The average shift of the oesophagus ranged from 2.7 ± 2.2 to 5.0 ± 3.5 mm. The average real-time oesophageal shift ranged from 2.7 ± 2.2 to 3.8 ± 3.4 mm. No significant shift was detected until the 90th minute of the procedure. The average shift of the 3D model of the LA and the oesophagus ranged from 1.4 ± 1.8 to 3.3 ± 3.0 mm (right-left direction) and from 0.9 ± 1.2 to 2.2 ± 1.3 mm (craniocaudal direction). During the 2 h procedure, there were no significant shifts of the model., Conclusion: During catheter ablation for atrial fibrillation, there is no significant change in the position of the oesophagus until the 90th minute of the procedure and no significant shift in the 3D model of the LA and the oesophagus. The 3D model of the oesophagus reliably depicts the position of the oesophagus during the entire procedure., (Published on behalf of the European Society of Cardiology. All rights reserved. © The Author 2016. For permissions please email: journals.permissions@oup.com.)

Published
2017
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