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# Current Directions in Biomedical Engineering

### Joint Journal of the German Society for Biomedical Engineering in VDE and the Austrian and Swiss Societies for Biomedical Engineering

Editor-in-Chief: Dössel, Olaf

Editorial Board: Augat, Peter / Buzug, Thorsten M. / Haueisen, Jens / Jockenhoevel, Stefan / Knaup-Gregori, Petra / Kraft, Marc / Lenarz, Thomas / Leonhardt, Steffen / Malberg, Hagen / Penzel, Thomas / Plank, Gernot / Radermacher, Klaus M. / Schkommodau, Erik / Stieglitz, Thomas / Urban, Gerald A.

CiteScore 2018: 0.47

Source Normalized Impact per Paper (SNIP) 2018: 0.377

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Online
ISSN
2364-5504
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Volume 2, Issue 1

# An algorithm to automatically determine the cycle length coverage to identify rotational activity during atrial fibrillation – a simulation study

Wenzel Kaltenbacher
/ Markus Rottmann
/ Olaf Dössel
Published Online: 2016-09-30 | DOI: https://doi.org/10.1515/cdbme-2016-0038

## Abstract

Atrial fibrillation is the most common cardiac arrhythmia. Many physicians believe in the hypothesis that persistent atrial fibrillation is maintained by centers of rotatory activity. These so called rotors are sometimes found by physicians during catheter ablation or electrophysiological studies but there are also physicians who claim that they did not find any rotors at all. One reason might be that today rotors are mainly identified by visual inspection of the data. Thus we are aiming at an algorithm for rotor detection. We first developed an algorithm based on the local activation times of the intracardiac electrograms recorded by a multielectrode catheter that can automatically determine the cycle length coverage. This was done to get an objective view on possible rotors and therefore help to quantify whether a rotor was found or not. The algorithm was developed and evaluated in two different simulation setups, where it could reliably determine cycle length coverage. But we found out that effects like wave collision and slow conduction have strong influence on cycle length coverage. This prevents cycle length coverage from being suited as the only parameter to quantify whether a rotor is present or not. On the other hand we could confirm that rotors imply a cycle length coverage of >70% if the multielectrode catheter is centered in an area of <5 mm away from the rotor tip. Therefore cycle length coverage can at least be used in some situations to exclude the presence of possible rotors.

## 1 Introduction

Many physicians state that persistent atrial fibrillation (AF) is maintained by centers of rotatory activity [1], [2]. On the other hand there is a large number of physicians however, who do not find any rotors at all. A possible reason could be, that in clinical systems there are no quantitative methods there is a rotor or not. Therefore we developed an algorithm that determines the cycle length coverage (CLC) automatically aiming at a method for automatic rotor detection.

CLC is a parameter that is also used by physicians but it is only estimated by visual inspection of the multichannel electrograms. With our algorithm we want to bring new objective information to the discussion about rotors and reduce subjective influences that complicate the discussion. The algorithm is based on the local activation times (LATs) that are determined by detection of the steepest negative slope of the measured electrograms.

## 2.1 Simulation setup

We used the Nygren cardiac cell model and created a 3D tissue patch with a size of 100 × 100 mm and a voxel side length of 0.1 mm [3]. The monodomain equations were solved with the parallel solver aCELLerate [4]. By forward calculation extracellular potentials were calculated with a sampling rate of 1000 Hz. A voltage map of this simulation is shown in Figure 1.

Figure 1:

Voltage map of the rotor in the 3D patch with a Lasso catheter (diameter 20 mm) and the measured electrograms for two different positions. Red circles mark the LATs. CLC in the first measurement is about 90% and 20% in the second measurement.

Figure 2:

DF determination algorithm: (A) Electrograms measured by one electrode, several cycles long. (B) Frequency spectrum calculated by discrete Fourier transform. (C) Modified spectrum calculated by adding the next five harmonics to each base frequency.

Furthermore the algorithm was implemented in a 3D atria model that is based on the Courtemanche-Ramirez-Nattel model that was adjusted to chronic AF cardiac cells for AF simulation. The 3D atria model includes fiber orientation and is built by 263 × 328 × 283 voxels with an edge length of 0.33 mm [5], [6].

## 2.2 Cycle length coverage

As already mentioned CLC is a parameter that is also used by physicians and is based on the LATs of the electrograms that are measured by a multielectrode catheter on the endocardium. It describes the time that a propagating wave takes to fully pass the catheter in proportion to the CL. In Figure 1 the electrograms for two different catheter positions on the 3D patch are shown. The LATs are marked with red circles in the electrograms. CLC is calculated by

$CLC=Last⁢LAT−First⁢LATCycle⁢Length.$(1)

The resulting CLCs correspond to the relation between the red arrow and the black arrow. In case that the catheter is centered on the rotor a line-shaped LAT pattern with a high CLC of 90% results, whereas CLC is only 20% if the catheter is passed by a nearly planar wave as in the second position [4]. To determine the cycle length (CL) and LATs that are required for CLC determination several steps are taken:

The dominant frequency is roughly the inverse the CL. Therefore DF−1 is used as first guess of CL (chapter 2.3). In the second step CL is determined precisely as the time difference between two consecutive LATs (chapter 2.4). In the third step CLC is calculated. This has to be done in a time window that only contains LATs from one propagation wave. Several CLCs in different time windows are calculated to find this specific time window (chapter 2.5).

## 2.3 Dominant frequency determination

For precise CL calculation two consecutive LATs have to be determined. However, the LAT determination with the steepest negative slope, will deliver more time stamps within one activation. Therefore DF−1 is used as first guess of CL to limit the time window to a length where only one LAT might be included.

The DF is defined as the highest amplitude of the frequency spectrum of a signal. The frequency spectrum can be calculated by discrete Fourier transform of the measured signal that is several cycles long.

Sometimes the spectrum has large peaks at one of the harmonics as well and not only at the base frequency. Therefore the next five harmonics of each frequency are added to the base frequency to get a new spectrum, where the harmonics of each frequency contribute to the basic frequency. If —S(f)— describes the initial spectrum, the modified spectrum is calculated with

$Smod⁢(f)=∑i=05S⁢(i⋅f)$(2)

## 2.4 Cycle length determination

The CL describes the duration between two action potentials passing one electrode. If a catheter is centered upon a rotor, the CL is also the duration of one rotation.

To determine the instantaneous CL, first an LAT in a time window with a length of DF−1 is determined. Then the following LAT is sought. Therefore the start of the next time window that is to be analyzed is set to first LAT + 1/3 DF−1. From there again the LAT in a time window of DF−1 is determined. It is assumed, that the time window of 1/3 DF−1 after the first LAT does not contain the second LAT. It is skipped to avoid false LATs that would result from another activity of the first propagation wave. The instantaneous cycle-specific CL is then calculated with

$CL=LAT2−LAT1$(3)

## 2.5 Automatic cycle length coverage calculation

With the algorithm of chapter 2.2 the CL at every electrode can be calculated. For CLC calculation we take the median of the CLs of all electrodes. The signals are then all windowed to the length of this CL, beginning with the same start time. In the next step the LAT of each electrode in this common time window is determined.

To determine the correct CLC it is important to analyze the correct time window where all LATs are from the same wave propagation. Figure 3A shows a high CLC that is formed by LATs from two waves. If the LATs are from two consecutive propagation waves the CLC is always high regardless of whether a rotor is near to the catheter or not. This leads to a pattern as depicted in Figure 3A. The correct CLC is shown in Figure 3B. To determine the correct CLC, several CLCs are calculated with a varying start time of the time window. For the first CLC N LATs were determined with N being the number of electrodes. The start of the following time windows is continuously shifted between these LATs. The algorithm is illustrated in the flowchart in Figure 4. For the calculation of the second CLC (k =2), the begin of the time window is shifted to

$tstart,k=LATi⁢k−1+LATk2$(4)

Figure 3:

LAT: red dot; CL: black arrow; time difference between first and last LAT: red arrow. (A) The LATs in this time window are composed from LATs of two propagation waves. A false CLC >90% results. (B) The LATs are now all from one propagation wave. The calculated CLC is about 40%, which is the correct CLC.

Figure 4:

Flowchart of the algorithm to determine the CLC in the correct time window.

Again the LATs for each electrode are determined and the CLC is calculated. This is repeated until tstart,10 is reached and 10 CLCs are calculated (in case of a catheter with 10 electrodes). The correct time window, where all LATs are from one propagating wave, is found when CLC is minimal.

## 3 Results

We analyzed the CLC as a function of the distance between catheter center and rotor center to see how close a physician has to be to the rotor center to be able to detect the rotor using only the CLC.

The results, obtained from the 3D patch, where no disturbing effects were present, showed a clear relationship between CLC and the distance between catheter and rotor, only depending on catheter size, electrode number and geometry. One example is given in Figure 5. A CLC of more than 70% could only be obtained in the area around the rotor. Unfortunately this clear relationship could not be confirmed in the 3D atria model.

Figure 5:

Function of CLC and distance between catheter and rotor tip for the undisturbed signals on the patch.

Due to wave collisions, areas of low CV and a heterogeneous excitation, the CLC could also be high even if the catheter was placed 20 mm away from the rotor tip. A high CLC did not imply a rotor near the catheter. The assumption of the inverse case – namely that CLC is always increased if the catheter is centered near to a rotor could be confirmed though. A high CLC is a necessary but not suficient condition to give a clear statement whether a rotor is near the catheter. However a low CLC can give at least evidence that no rotor is present right next to the catheter.

## 4 Limitations and discussion

In our simulations the presented algorithm was able to determine CLC reliably. However, one possible limitation of the algorithm to determine instantaneous CL is, that an abrupt change of CL to more than 1.33 times the DF−1 would lead to a second LAT that would lay outside the time window in which the LATs are determined. Therefore strong changes of CL would lead to false values of CLC. In our simulations, morphology of the activation measured at the electrodes was almost constant over time. In clinical cases morphology of the signals can vary strongly, therefore the algorithm to determine the DF may have to be improved.

The fact, that CLC determination alone was not sufficient for clear rotor detection shows that a combination of several methods is necessary for rotor identification. LAT pattern analysis as well as analysis of signal characteristics might improve the reliability of the automatic rotor identification.

## Author’s Statement

Research funding: The author state no funding involved. Conflict of interest: Authors state no conflict of interest. Material and Methods: Informed consent: Informed consent is not applicable. Ethical approval: The conducted research is not related to either human or animal use.

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Published Online: 2016-09-30

Published in Print: 2016-09-01

Citation Information: Current Directions in Biomedical Engineering, Volume 2, Issue 1, Pages 167–170, ISSN (Online) 2364-5504,

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