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BACKGROUND: Recent studies have demonstrated conflicting mechanisms underlying atrial fibrillation (AF), with the spatial resolution of data often cited as a potential reason for the disagreement. The purpose of this study was to investigate whether the variation in spatial resolution of mapping may lead to misinterpretation of the underlying mechanism in persistent AF. METHODS AND RESULTS: Simulations of rotors and focal sources were performed to estimate the minimum number of recording points required to correctly identify the underlying AF mechanism. The effects of different data types (action potentials and unipolar or bipolar electrograms) and rotor stability on resolution requirements were investigated. We also determined the ability of clinically used endocardial catheters to identify AF mechanisms using clinically recorded and simulated data. The spatial resolution required for correct identification of rotors and focal sources is a linear function of spatial wavelength (the distance between wavefronts) of the arrhythmia. Rotor localization errors are larger for electrogram data than for action potential data. Stationary rotors are more reliably identified compared with meandering trajectories, for any given spatial resolution. All clinical high-resolution multipolar catheters are of sufficient resolution to accurately detect and track rotors when placed over the rotor core although the low-resolution basket catheter is prone to false detections and may incorrectly identify rotors that are not present. CONCLUSIONS: The spatial resolution of AF data can significantly affect the interpretation of the underlying AF mechanism. Therefore, the interpretation of human AF data must be taken in the context of the spatial resolution of the recordings.
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Recent studies have demonstrated conflicting mechanisms
underlying persistent atrial fibrillation (AF), with the spa-
tial resolution of data often cited as a potential reason for the
disagreement. The hierarchical model of AF states that dis-
turbances are sustained by drivers, in the form of rotors or
focal sources.1 Evidence for rotors as drivers of human AF is
inferred from termination through ablation of putative stable
rotor sites, mapped with basket catheters,2,3 as well as ablation
of regions with a high probability of transient rotors, identi-
fied using a noninvasive body surface mapping technology.4
Despite these data, the rotor paradigm is neither confirmed
nor universally accepted,5–7 with recent studies raising ques-
tions about the efficacy of rotor-targeted ablation.8,9 The con-
trasting multiple-wavelet hypothesis of AF, proposed by Moe
et al10 in the 1960s, states that AF is sustained by multiple,
self-perpetuating, randomly propagating activation wavelets.
This is supported by Allessie et al11 and de Groot et al12 who
found no evidence for the presence of stable focal sources or
rotors using a small high-resolution spoon-shaped mapping
device. Similarly, the Waldo laboratory found no evidence of
rotational activity using an epicardial electrode array (inter-
electrode spacing, 5.2–7.0 mm); in this case, AF was main-
tained by wavefronts from foci and breakthrough sites.13
These contradictory results have spawned intense debate5,7
with findings attributed to the divergent methods used. One
source of variation arises from differences in scale (global
versus regional) and electrode density and therefore spatial
resolution of the mapping techniques. A second difference is
the approach used to analyze fibrillatory wavefront dynam-
ics, using either phase mapping14 or activation time.12 Correct
Circ Arrhythm Electrophysiol is available at DOI: 10.1161/CIRCEP.116.004899
Original Article
Background—Recent studies have demonstrated conflicting mechanisms underlying atrial fibrillation (AF), with the spatial
resolution of data often cited as a potential reason for the disagreement. The purpose of this study was to investigate
whether the variation in spatial resolution of mapping may lead to misinterpretation of the underlying mechanism in
persistent AF.
Methods and Results—Simulations of rotors and focal sources were performed to estimate the minimum number of
recording points required to correctly identify the underlying AF mechanism. The effects of different data types (action
potentials and unipolar or bipolar electrograms) and rotor stability on resolution requirements were investigated. We also
determined the ability of clinically used endocardial catheters to identify AF mechanisms using clinically recorded and
simulated data. The spatial resolution required for correct identification of rotors and focal sources is a linear function
of spatial wavelength (the distance between wavefronts) of the arrhythmia. Rotor localization errors are larger for
electrogram data than for action potential data. Stationary rotors are more reliably identified compared with meandering
trajectories, for any given spatial resolution. All clinical high-resolution multipolar catheters are of sufficient resolution
to accurately detect and track rotors when placed over the rotor core although the low-resolution basket catheter is prone
to false detections and may incorrectly identify rotors that are not present.
Conclusions—The spatial resolution of AF data can significantly affect the interpretation of the underlying AF mechanism.
Therefore, the interpretation of human AF data must be taken in the context of the spatial resolution of the recordings.
(Circ Arrhythm Electrophysiol. 2017;10:e004899. DOI: 10.1161/CIRCEP.116.004899.)
Key Words: ablation techniques arrhythmias, cardiac atrial fibrillation
computational modeling reentry rotor
Received December 20, 2016; accepted April 11, 2017.
From the ElectroCardioMaths Programme (C.H.R., C.D.C., N.A.Q., P.B.L., P.K., N.S.P., F.S.N.), and the Department of Bioengineering (J.H.T.), Imperial
College London, United Kingdom; IHU Liryc, Electrophysiology and Heart Modeling Institute, Fondation Bordeaux Université, Pessac-Bordeaux, France
(J.D.B., E.J.V.); and Université de Bordeaux, IMB, UMR 5251, Talence, France (J.D.B., E.J.V.).
*Drs Vigmond and Ng contributed equally to this work.
The Data Supplement is available at
Correspondence to Nicholas S. Peters, MD, Imperial College London, 4th Floor Imperial Centre for Translational and Experimental Medicine,
Hammersmith Campus, Du Cane Rd, London W12 0NN, United Kingdom. E-mail
© 2017 The Authors. Circulation: Arrhythmia and Electrophysiology is published on behalf of the American Heart Association, Inc., by Wolters Kluwer
Health, Inc. This is an open access article under the terms of the Creative Commons Attribution Non-Commercial-NoDerivs License, which permits
use, distribution, and reproduction in any medium, provided that the original work is properly cited, the use is noncommercial, and no modifications or
adaptations are made.
Spatial Resolution Requirements for Accurate
Identification of Drivers of Atrial Fibrillation
Caroline H. Roney, PhD; Chris D. Cantwell, PhD; Jason D. Bayer, PhD;
Norman A. Qureshi, MRCP, PhD; Phang Boon Lim, MRCP, PhD; Jennifer H. Tweedy, PhD;
Prapa Kanagaratnam, PhD; Nicholas S. Peters, MD; Edward J. Vigmond, PhD*; Fu Siong Ng, MRCP, PhD*
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2 Roney et al Spatial Resolution Requirements During AF
interpretation of AF mechanisms is critical for effective diag-
nosis and delivery of ablation therapy.
In this study, we systematically investigated the hypothesis
that the variation in spatial resolution of mapping systems may
lead to misinterpretation of mechanism in persistent AF. We
determined, through computer simulation, the minimum reso-
lution required to accurately identify rotors and focal sources
and to avoid false detections, using unipolar and bipolar recon-
structed electrograms from 5 clinical catheter configurations.
These were compared against action potential data requirements
for computational modeling data. We considered stationary
versus meandering rotors. Finally, we compared clinical phase
maps and detected singularities for data measured during AF.
The Methods are briefly described here with full details in the Data
Simulation Data
We initially determined resolution requirements on a regularly
spaced 2-dimensional (2D) homogeneous grid for a stable rotor or
focal source, before testing on more complicated arrhythmias with
spatially varying activation and repolarization properties, realistic ge-
ometries, and catheter electrode arrangements.
Monodomain simulations of rotors and focal sources were per-
formed using the Courtemanche-Ramirez-Nattel human atrial cell
model, with changes representing electrical remodeling in AF.15 To
generate a physiological range of spatial wavelengths in a 10 cm×10
cm sheet, the conduction velocity (CV)16 and local atrial rate17,18 were
varied by modifying tissue diffusivity (0.0005, 0.001, and 0.0015
cm2/ms) and IK1 conductance (gK1; 0.09, 0.135, and 0.18 nS/pF), re-
sulting in CVs of 0.26, 0.36, and 0.43 m/s and action potential (AP)
durations of 121, 142, and 181 ms (considered as 9 combinations;
Tables I and II and Section 1.1.1 in the Data Supplement).
The effects of simulated data type and rotor stability were test-
ed using an atrial bilayer model.19,20 These simulations included
interstitial fibrosis as microstructural discontinuities,20 with distribu-
tions based on late-gadolinium intensity values from patients with
persistent AF21 used to infer probabilities for fibrosis inclusion in
the model, resulting in heterogeneous anisotropic conduction. For 1
simulation, areas of fibrosis also included reduced conductivity and
changes to the ionic properties. Unipolar electrograms were calculat-
ed 1 mm off the endocardium with bipolar electrograms calculated as
differences between paired unipoles with 4 mm spacing. Full model
details are given in Section 1.1.2 in the Data Supplement.
High-density catheters were simulated, including a circular
(Lasso), spiral (AFocus II), and 2 variations of a 5-spline (PentaRay)
catheter with different interelectrode spacings, all of diameter 2 cm.
Lower resolution basket catheters (median interelectrode spacing,
10.2 mm; lower quartile, 5.9 mm; upper quartile, 16.2 mm) were
simulated in an anatomically accurate human left atrial model for 30
seconds of AF for 2 parameter sets, corresponding to short (45.2 mm)
and long (75.2 mm) wavelength activity (Section 1.1.3 in the Data
Clinical Data
All data were obtained with informed consent under ethical ap-
proval from the UK Health Research Authority Ref 13/LO1169.
Electrograms and electrode locations were recorded during AF from
the left atrium of 11 patients (6–17 catheter recording locations per
patient; 127 total) at the beginning of ablation procedures, using mul-
tipolar AFocus II catheters and the Ensite Velocity electroanatomic
mapping system (St Jude Medical, Inc). Unipolar and bipolar electro-
grams were recorded for 16 to 106 seconds (mean, 34 seconds). To in-
vestigate the effects of resolution on phase singularity (PS) detection,
analysis was performed for random subsets of 4 to 19 electrograms,
and the number of missing and false PS detections were calculated.
Identifying Rotors and Focal Sources
Figure 1A outlines our methodology. AP and bipolar and unipolar
electrogram data were downsampled, phase was calculated for each
modality22 and interpolated, singularities were identified, and statis-
tics were calculated on a regional basis. PSs were located by calculat-
ing the topological charge23 and were tracked over time, with those
lasting >120 ms defined to be rotors.20
Resolution requirements were determined for the 10 cm×10 cm
sheet by uniformly spatially downsampling voltage data to different
resolutions, ranging from 1 to 25 mm. For the atrial bilayer model,
we considered subsets of nodes corresponding to the average distance
between nodes, termed mesh resolution (MR), of 1.62 to 17.1 mm.
To compare results between different resolutions, downsampled
phase (uniformly downsampled resolutions: 1–25 mm) was in-
terpolated using cubic splines to full grid resolution (0.1 mm) for
the 2D sheet (Figure 1B) or to 1.62 mm MR for the bilayer model
(MR=1.62–17.1 mm, 4813–36 points). Phase rather than voltage was
interpolated (Section 1.2 in the Data Supplement) because electro-
grams vary in magnitude (particularly bipoles) making their interpo-
lation challenging.
For focal source identification, we calculated the divergence of
the CV field24 (Figure I in the Data Supplement). For each AP, activa-
tion time was calculated as the location of the maximum temporal
derivative. CV vectors were calculated by differencing the activation
times of four neighboring points.25 The point of maximum divergence
of the normalized CV field identified the origin of focal sources.
Criteria for Determining Required Resolutions
The accuracy of rotor identification was assessed using 2 measures:
(1) visual inspection of isopotential plots over time and (2) error in the
center of the rotor trajectory calculated using phase (time-averaged
center error criterion; success if within an ablation catheter diameter
of 4 mm). For (2), PS locations were calculated as detailed above.
To separate these PSs into rotor PSs and false detections, a rotor PS
was seeded in an initial frame of the simulation and tracked over time
subject to a movement threshold to detect rotor PSs over the simu-
lation duration. Other PSs were then defined to be false detections
It is unclear whether the different reported causes of
persistence of atrial fibrillation—focal and rotational
drivers, and multiple wavelets—are the result of dif-
ferent underlying mechanisms or result from different
scales and resolutions of recording devices and inter-
pretations of the electrographic data they produce.
This study determined the minimum resolution re-
quired to accurately identify rotors and focal sources,
and to avoid false detections, as a function of the spa-
tial wavelength (the distance between wavefronts) of
the arrhythmia.
Stationary rotors are more reliably identified com-
pared to meandering trajectories, for any given spa-
tial resolution.
All clinical high-resolution multipolar catheters are
of sufficient resolution to accurately detect and track
rotors when placed over the rotor core, though the
low-resolution basket catheter is prone to false de-
tections and may incorrectly identify rotors that are
not present.
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3 Roney et al Spatial Resolution Requirements During AF
(Figure 2B). To assess the influence of false detections on correct
rotor identification, both the number and distribution of falsely identi-
fied PSs were assessed.
A methodology for determining an appropriate threshold for the
number of permissible false detections was developed by consider-
ing the number of PSs as a function of distance from the true rotor
core location, which was taken to be the time-averaged full-resolution
rotor core location (Figure 2C). A resolution is considered to fail the
false PS detection histogram criterion if the resulting histogram con-
tains multiple peaks (Figure 2F), corresponding to additional spatial
clusters of PSs that represent false detections. These spatial clusters
could be misidentified as rotor locations.
Example resolutions for which identification is successful and un-
successful for each of the 3 criteria are shown in Figure 2.
Figure 1. Methods schematic. A, Action potential (AP) data were computed at a mesh resolution (MR) of 0.34 mm edge length (93 927
points). Data were then downsampled: 1.62 to 17.1 mm (4813–36 points). Voltages were interpolated (to MR=1.62 mm), and phase was
calculated. Unipolar electrograms were calculated at AP point distribution. Bipolar electrograms were calculated from paired unipolar
electrograms with 4-mm interelectrode spacing. Phase of unipolar and bipolar electrograms was calculated and interpolated to MR=1.62
mm. Phase singularities were tracked over time (>120 ms trajectories tagged as rotors), and regional assessment was performed. B, A
mapping is introduced for phase interpolation. Direct interpolation of the phase angle θ leads to issues when interpolating, in the instance
that neighboring points are close to π and −π (left). Mapping to the exponential form (eiϑ), interpolating this and then converting back to a
phase angle, removes the issue with phase angle discontinuities (right). The errors become larger as the grid spacing is increased (bot-
tom). The domain size shown here is 10 cm-by-10 cm.
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4 Roney et al Spatial Resolution Requirements During AF
Focal sources were identified using the same measures as for ro-
tors, except the center of the focal source was identified using the
maximum divergence of the velocity. There were no false detections
of positive divergence.
Wavelength Estimation
We express resolution requirements in terms of the number of record-
ing points (N) needed within 1 spatial wavelength (λ), the distance
between consecutive wavefronts.
Figure 2. Methodology for defining success or failure of rotor identification. Left column (A, C, and E): successful identification at 7-mm
spacing; right column (B, D, and F): failed identification at 17-mm spacing. A and B, Phase singularity (PS) locations corresponding to the
rotor core (green) and false detections (red and blue, coloured depending on spin). C and D, Rotor core PSs (green), showing the time-
averaged center of the full-resolution rotor trajectory (black) and the time-averaged center of the given resolution rotor trajectory (purple).
The distance between these gives the time-averaged center error (C: 0.9 mm, success; D: 4.3 mm, failure of the time-averaged center
error criterion). E and F, Histogram of number of PSs plotted as a function of distance from the full-resolution time-averaged rotor center.
At 7 mm (E), there is a single peak corresponding to the true rotor center, whereas at 17 mm (F), there are 2 peaks in the histogram corre-
sponding to a failure of the false PS detection histogram criterion because the false detections may be misidentified as a rotor core.
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5 Roney et al Spatial Resolution Requirements During AF
The wavelength associated with each parameter set was automati-
cally determined from full-resolution data by calculating the distance
between arms of spiral wavefronts of a rotor or consecutive circular
wavefronts of a focal source, using isopotential lines26 (Figure 3A;
Section 1.4.1 in the Data Supplement).
Where measurements are sparse, we define λ as the product of
mean CV (Section 1.4.2 and Figure II in the Data Supplement) and
mean cycle length: λ≈CV×cycle length. For bilayer simulations, λ
was estimated for all nodes at MR=1.62 mm by calculating mean CV
and cycle length over the simulation duration for data within a 2-cm
Resolution Required for Correct Identification of
Rotors and Focal Sources Is a Function of Spatial
For each assessment criteria, the minimum measuring points,
N, per wavelength was determined for each sheet simulation
parameter set, as the reciprocal of the gradient of the line of
best fit for each identification criterion. Figure 3B illustrates
that resolution and wavelength clearly influence the accuracy
of rotor core detection. We found that N=2.5 for visual iden-
tification, N=2.7 for the time-averaged center error criterion,
and N=3.1 for the false PS detection histogram criterion, as
shown in Figure 3C.
There must necessarily be a 3×3 grid of measuring points
between consecutive wavefronts for focal source identification
using maximum divergence to be successful. Because the dis-
tance between wavefronts decreases for shorter wavelengths,
correspondingly finer grid spacing is necessary (Figure III in
the Data Supplement). For accurate identification, N=3.3 for
visual inspection and N=1.6 when using the maximum diver-
gence criterion (Figure 3D).
Rotor Localization Errors Are Larger for
Electrogram Data Than for AP Data
Figure 4A shows an area of high PS density in an area of
high fibrosis in an anatomically accurate simulation of 2
rotors. Wavelength varies spatially (range, 21.5–108.1; mean
67.8±15.5 mm) because of the heterogeneous CV (range,
0.12–0.60 m/s; mean 0.37±0.09 m/s), where slow conduction
is seen in areas of high fibrosis. The 3 modeled elements of
fibrosis all decreased CV. As such, resolution requirements
also varied spatially.
For a given resolution, Figure 4B shows that PS distribu-
tions were visually similar across data types, as were the num-
ber of PSs, number of rotors and rotor duration, as shown in
Figure 4C. For computational efficiency, electrograms were
only calculated at MR1.6 mm, whereas AP interpolation was
only calculated for MR3.5 mm. The mean localization error
was generally higher for both types of electrogram phase than
for AP phase. Results for AP phase were similar when using
either voltage or phase interpolation.
Stationary Rotors Are More Reliably Identified
Compared With Meandering Trajectories
We analyzed simulation data in which 1 rotor anchored to an
area of high fibrosis intensity on the posterior wall (Figure 5A,
compare PS density and late gadolinium enhancement maps),
and a second rotor meandered across the anterior wall cover-
ing a larger area (Figure 5B). The CV is again heterogeneous
(range, 0.21–0.59 and 0.44±0.08 m/s), leading to heteroge-
neous wavelength (39.7–110.1 and 81.2±13.9 mm), with
shorter wavelengths in areas of fibrosis (Figure 5A).
On reducing resolution, PSs are still identified near the
stable rotor, but the meandering rotor trajectory breaks up
with both AP and unipolar data (Figure 5B). This is apparent
in the regional analysis (Figure 5C) in which region 3, cor-
responding to the stable rotor, is a high driver region across
all resolutions (top PS region for AP data for all resolutions),
whereas regions 5 and 6, corresponding to the meandering
rotor, decrease in importance for MR11.9 mm for AP data.
The average number of PSs and rotors detected decreased
with coarser MR (Figure 5D) as did rotor duration (Figure 5E).
PS location error increased at coarser MR for all data types.
Multipolar Catheters Are of Sufficient Resolution to
Accurately Detect and Track Rotors If Placed Over
the Rotor Core
We investigated whether electrode arrangements of com-
monly used high-density clinical mapping catheters satisfy
the resolution requirements identified above for reliably iden-
tifying rotors at the shortest wavelength (33.6 mm). Illustra-
tive isophase maps and rotor core PS trajectories are shown in
Figure 6A.
For 20 unipole configurations, the circular (Lasso) catheter
produced the largest time-averaged center location error (3.5
mm) with respect to full-resolution (0.1 mm) simulated data.
Other catheters gave significantly lower errors (Figure 6B).
Corresponding frame-wise errors in PS location are shown in
Figure 6C, where the circular catheter again had the largest
For the 10 bipole configuration, formed from 20 unipolar
signals, the spiral (AFocus II) catheter produced the smallest
location errors (quantified in Figure 6B and 6C). The circu-
lar catheter gave similar errors with either 20 unipoles or 10
bipoles, whereas the accuracy of the other catheters decreased
as the number of data points was reduced.
Low-Resolution Basket Catheters Are Prone to
False Detections
In contrast to the high-density catheters examined above,
basket catheters provide global coverage at a lower electrode
density.2 Geodesic distances between each basket electrode
and its 4 neighboring electrodes are shown in Figure 7A. The
majority of interelectrode distances satisfy our requirements
for accurately locating rotor cores (time-averaged center error
criterion): 99.1% for the longer wavelength (75.2 mm) resolu-
tion requirement of 27.9 mm (75.2/2.7=27.9) and 79.3% for
the shorter wavelength (45.2 mm) resolution requirement of
16.7 mm. Fewer interelectrode distances satisfied the require-
ments to avoid false detections (false PS detection histo-
gram criterion): 96.4% for the longer wavelength resolution
requirement of 24.4 mm and 64.0% for the shorter wavelength
resolution requirement of 14.5 mm.
Interpolated phase maps were qualitatively similar to
the high-resolution phase maps, as shown in Figure 7C
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6 Roney et al Spatial Resolution Requirements During AF
and 7E. The rotor core was accurately located for the short
wavelength simulation (1.3 mm time-averaged center
error). For the long wavelength simulation, 2 rotor cores
were present in the mapping area for much of the simu-
lation. The first was located with sufficient accuracy (3.6
mm time-averaged center error; 2.6% of frames missing
Figure 3. Resolution requirements for spiral wave detection and focal source detection depend on spatial wavelength. A, Technique to
calculate wavelength of a spiral or focal wavefront. Isopotential lines at −60 mV with positive (green) and negative (blue) gradient. Inter-
sections of the ray (white line) with the isopotential lines of positive gradient are shown (purple dots). B, Distributions of PSs over time for
rotor simulations at different resolution and wavelengths. Phase singularities corresponding to a rotor core location are shown in green.
Number of false detections (chirality shown in blue and red) increased as wavelength decreased and as grid spacing increased. C, Mini-
mum N necessary to identify a rotor for each criterion. D, Minimum N necessary to identify a focal source for each criterion.
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7 Roney et al Spatial Resolution Requirements During AF
rotor core detections), whereas the second rotor had a time-
averaged center error greater than the 4-mm threshold (5.4
mm) because many PSs were along the edge of the full-
resolution area of coverage and as such were not picked up
by the basket arrangement (40.2% of frames missing rotor
core detections).
For the short wavelength simulation, many false detections
were observed. For example, Figure 7G shows an additional
cluster of PSs close to the main rotor for the short wavelength
simulation. This aligned with a larger interelectrode spacing
between electrodes vertically. Subsequently, this led to a sec-
ondary peak in the PS distribution histogram (Figure 7H).
When a basket catheter with double the number of splines
(ie, 16 splines of 8 electrodes) was simulated, the cluster of
false detections was no longer present, as shown in Figure 7J
and 7K.
In addition, the average rotor path is accurate; however, the
PS trajectory showed a larger rotor meander area for the bas-
ket resolution data than for the high-resolution data (Section
2.3 and Figure IV in the Data Supplement).
Figure 4. Phase singularity (PS) distributions and characteristics for different data modalities. A, Normalized late gadolinium enhance-
ment (LGE)-magnetic resonance imaging data for a patient with persistent atrial fibrillation was used to infer probabilities for fibrosis
inclusion in the model; high PS density is seen to coincide with high fibrosis density; PS locations over time show rotor trajectories; wave-
length varies spatially. B, Comparison of detected PS locations for mesh resolutions (MRs) of 3.52 mm (top) and 13.6 mm (bottom), for
different AP interpolations and electrogram modalities. C, Number of PSs (solid lines) and rotors (dashed lines), (D) rotor durations, and (E)
distance errors as a function of MR.
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8 Roney et al Spatial Resolution Requirements During AF
Figure 5. Stationary rotors are more reliably identified compared with meandering trajectories. A, Average late gadolinium enhancement
(LGE)-magnetic resonance imaging map, phase singularity (PS) density, and local wavelengths, as well as numbered regions used for
regional analysis. B, PS distributions shown on the posterior (top) and anterior (bottom) walls for different resolutions and modalities. C,
Regional analysis showing mean number of phase singularities and rotors in each region (error bars indicate SD for the number of phase
singularities). D, Number of PSs (solid lines) and rotors (dashed lines), (E) rotor durations, and (F) distance errors as a function of mesh
resolution (MR).
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9 Roney et al Spatial Resolution Requirements During AF
Figure 6. Multipolar catheters are of sufficient resolution to accurately detect and track rotors. A, Top: Example isophase maps interpo-
lated from the recording points shown in black (I–IV), with the phase from the full-resolution simulation data shown in (V). Bottom: Rotor
core phase singularity (PS) trajectories for each catheter type calculated using the interpolated phase. Examples are shown for spiral
(AFocus II), circular (Lasso), and 2 five-spline electrode arrangements (PentaRay I and PentaRay II). B, Errors in the time-averaged esti-
mated center location compared with the time-averaged location computed from the raw simulation data. Catheters are configured as
either 20 unipoles or 10 bipoles. C, Box plots to show frame-wise difference in estimated PS location compared with the location com-
puted from raw simulation data. The boxes indicate the interquartile range (IQR) and median (red line) of the data; the whiskers extend to
a maximum of 1.5×IQR; and the crosses represent outliers.
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10 Roney et al Spatial Resolution Requirements During AF
For Clinical AF Data, Reducing the Number of
Electrodes in Mapping Catheters Increased the
Number of Missing and False PS Detections
We determined the ability of multipolar catheters to detect
PSs as electrodes were removed. Clinical catheter recordings
with different degrees of rotational activity were analyzed,
ranging from planar activity to curved rotor cores: overall
mean number of PSs for unipolar catheters 0.47±0.20, range
0 to 0.91 and for bipolar 0.36±0.16, range 0 to 0.73. Figure 8
shows box plots for the percentage of missing PSs (percent-
age of full-resolution PSs not present in downsampled data)
and the percentage of false detections (percentage of downs-
ampled data PSs not present in full-resolution data), which
both increase as the number of recording points is reduced.
Figure 7. Low-resolution basket catheters are prone to false detections. A, Interelectrode distances in an 8-spline basket catheter. Reso-
lution requirements for avoiding false detections for the 2 wavelengths (45.2 and 75.2 mm) are marked. B, Example isopotential map for
longer wavelength simulation with basket electrodes marked. C, High-resolution phase map generated from phase at mesh vertices.
Phase singularity (PS) marked as a black dot. D, Phase of electrodes as arranged on a regular 8×8 grid. E, Interpolated phase from bas-
ket arrangement of electrodes. F, Rotor PS locations computed from high-resolution data (blue) and the 8-spline basket electrodes (red)
for the short wavelength simulation. Only PSs that correspond to the rotor are shown. G, All detected PSs of 8-spline basket catheter. H,
PS detection histogram for 8-spline catheter. I, Rotor PS locations, (J) all PSs, and (K) PS detection histogram for a simulated 16-spline
catheter—double the clinical resolution.
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11 Roney et al Spatial Resolution Requirements During AF
Main Findings
In this study, we demonstrated that sufficient spatial resolu-
tion is essential for the accurate detection of rotors and focal
sources and propose that insufficient resolution may be respon-
sible for the conflicting findings of recent human studies.2,12,27
An estimate of the resolution requirements as a function of the
spatial wavelength was found for spiral wavefronts (rotors)
and circular wavefronts (focal sources) using different criteria.
For regularly spaced grids, the minimum resolution required
is a ratio of spatial wavelength to number of measuring points
per wavelength (λ/N). For rotors, N=2.5 (visual inspection),
N=2.7 (rotor core time-averaged center error), and N=3.1
(to avoid false detections). For focal sources, N=3.3 (visual
inspection) and N=1.6 (maximum divergence calculation of
focal source origin location). The results suggest that although
the basket catheter has adequate resolution to track rotors, it
has inadequate resolution to avoid false detections.
We found that although stationary rotors may be identi-
fied at coarse resolutions, meandering rotors are lost. For atrial
bilayer simulations, regional analyses at all resolutions consid-
ered identified the same region as having the highest PS density,
whereas rotor localization error was unacceptable for MR11.9
mm. This suggests that standard mapping modalities offer suffi-
cient resolution for ablation guided by regional driver density27
although localization of meandering rotors may not be possible.
In addition, resolution requirements are similar for unipolar and
bipolar electrogram data. Correct PS identification for clinical
spiral (AFocus II) mapping catheter recordings is sensitive to
the number of electrodes used in the analysis.
Spatial Wavelengths in Human AF
We simulated 9 different wavelengths for rotors and focal
sources to determine the relationship between resolution
requirements and wavelength. Based on previous reports, the
expected range of spatial wavelengths in human AF is 44 to
127 mm, because of the varying degree of electric remodeling
in patients with AF. This range was estimated as CV divided
by dominant frequency, where CVs are in the range 0.38±0.1
to 0.61±0.06 m/s,16 and dominant frequency ranges from 4.8
to 8.6 Hz.17,18 The wavelengths of the spiral waves simulated
in this study cover a subset of this range from 33 to 78 mm.
Wavelength may vary spatially (Figures 4A and 5A) because
of conduction or repolarization heterogeneities, leading to
spatially varying resolution requirements. This is particularly
important as rotors may anchor to areas of slow conduction.
Away from a rotor core, 7 points were required for an accu-
rate and reliable estimate of spatial wavelength if located within
1 wavelength (Section 2.1 in the Data Supplement). High-density
mapping catheters fulfill this criterion because wavelengths in
human AF are estimated to be longer than their diameters.
Required Resolution for Regular Grids
The Nyquist criterion states that interelectrode spacing must
be less than half the smallest spatial wavelength of interest,28
corresponding to N=2. This study aimed to extend the work
of Rappel and Narayan,29 where a theoretical approach deter-
mined that the resolution required to identify stable rotors and
focal sources is of the form λ/N; their study identified wave
patterns visually and the required value of N was not quanti-
tatively determined. In our study, we find that the resolution
requirements are linear in λ, suggesting that the resolution
required does follow λ/N.
Four of the identification criteria suggest a slightly higher
value of N than the theoretical Nyquist criterion is needed in
practice, whereas the maximum divergence location suggests
a smaller value. This criterion was applied for focal sources
where the grid was centered over the focal source, which is the
optimal arrangement; off-center arrangements and placements
away from the source will require a higher N.
Required Resolution for Clinically Used Catheters
The most stringent spatial resolution requirement found for
identification of rotors in human AF is 44/3.1=14.2 mm. The
interelectrode spacings of all high-density mapping catheters
considered (AFocus II 4 mm, Lasso 6 mm, PentaRay 4 mm,
Figure 8. For clinical atrial fibrillation (AF) data, reducing the number of electrodes in high-density mapping catheters increased the
number of missing and false phase singularity (PS) detections. A, Box plots to show the percentage of full-resolution PSs not present in
downsampled data measured across 127 catheter recordings, for unipolar and bipolar electrode recordings. B, Box plots to show the per-
centage of PSs in downsampled data not present in full-resolution data. In all cases, the boxes indicate the interquartile range (IQR) and
median of the data (red line); the whiskers extend to a maximum of 1.5×IQR; and the crosses represent outliers.
by guest on May 17, 2017 from
12 Roney et al Spatial Resolution Requirements During AF
or 6 mm) are smaller than this distance, suggesting the ability
of these catheters to accurately locate PSs if placed over the
rotor core. For 20 recording points, the circular Lasso cath-
eter gave the largest error in estimating rotor center location
(Figure 6B). Similarly, Weber30 found that a simulated circu-
lar catheter performed worse than spiral and 5-spline cath-
eters because it could not identify focal sources, but rather,
the radial basis function interpolation showed a planar wave.
For clinical data, correct PS identification was sensitive to the
number of points used for interpolation from a high-density
spiral AFocus II mapping catheter (Figure 8).
A major disadvantage of mapping catheters is their local-
ized coverage; as such, rotor tracking is only possible if
the catheter is fortuitously placed over a rotor that does not
meander outside the margins of the catheter poles. If the cath-
eter does not lie over the rotor core, techniques presented by
Roney et al31 could be used to direct the catheter toward the
rotor, but these techniques are dependent on some degree of
organization of wavefronts remote from the driver. In addi-
tion, it may be necessary to consider the activity of surround-
ing electrograms to differentiate rotors from interactions
around lines of block.32
Unlike the catheters mentioned above, basket catheters
provide global coverage, which is a possible reason why stud-
ies using them2,33 were able to detect rotors in human AF,
whereas studies using catheters with only regional coverage7
were not. Our results confirm that basket catheters can accu-
rately detect rotors (Figure 7) and faithfully track PS trajecto-
ries (Figure IV in the Data Supplement).
Berenfeld and Oral33 comment that some areas of interpo-
lation for basket mapping have interspline difference of >20
mm; for the basket catheter used in this study, 12.6% of inter-
electrode distances are >20 mm. Laughner et al34 found that
equatorial bunching of basket catheter splines often occurred,
leading to a wide range of interspline distances within the bas-
ket, and this varied between patients. In addition, coverage of
the pulmonary veins, left septum, and left lateral wall was lim-
ited, with only 55% of the atrial surface covered, as observed
by Benharash et al,8 explaining the large number of missing
rotor detections in our study.
Low-Resolution Basket Catheters Are Prone to
False Detection of PSs
The basket catheter, however, was found to be inadequate
to avoid spurious rotors. Only 63.1% of the interelectrode
distances are less than the resolution requirement of 14.2
mm, corresponding to 3.1 points per spatial wavelength.
This is likely the cause of the false PS detections, where
the simulated basket data failed the false PS detection his-
togram criterion.
The tendency of basket catheters with inadequate resolu-
tion to detect nonexistent PSs may explain the discrepancy
between recent clinical studies, where studies using basket
catheters report stable rotors,2 whereas regional, higher-
resolution mapping do not report stable rotors.12,35 This may
explain, in part, the large incidence of rotors reported by
Narayan et al,2 a low termination rate,8 and poor long-term
success9 for ablating rotors detected by basket catheters. The
modeled 16-spline basket catheter did not suffer from false PS
detections although good endocardial contact of such a cath-
eter may be difficult to achieve in practice.
Our study comparing resolution requirements for station-
ary and meandering rotors found that rotor trajectories may be
lost at resolutions for which stable rotors are still identifiable
(Figure 5), which may explain differences in findings on rotor
stability with basket catheters identifying stable rotors and
noninvasive electrocardiographic imaging identifying tran-
sient meandering rotors.27,36
Effect of Datatype
Resolution requirements for AP, unipolar electrogram, and
bipolar electrogram data (Figure 4) were similar. Localization
errors were larger for electrogram data than for AP data and
always larger than the 4-mm threshold, corresponding to an
ablation catheter diameter, used for rotor location error, per-
haps also because of rotor meander and irregular point spacing
on the surface mesh (compared with the regular 2D grid).
The limitations of our study include (1) we assume the pres-
ence of rotors, (2) our tissue is simplified and we do not model
endocardial–epicardial dissociation. Furthermore, in the sim-
ulations for the clinically used catheters, all electrograms were
noise free, representing perfect data. In reality, electrograms
will contain noise, motion artifacts, and may have unsatisfac-
tory tissue contact.33
We determined the minimum spatial resolution requirements,
as a function of AF wavelength, to correctly identify the under-
lying AF mechanism. All clinically used catheters assessed in
our study possess adequate spatial resolution to identify and
track rotor core location for the range of wavelengths occur-
ring in human AF if covering the location of the rotor PS.
However, the low resolution of basket catheters renders them
prone to false detections. Resolution requirements depend on
rotor meander and AF spatial wavelength, but are similar for
AP, unipolar electrogram, and bipolar electrogram data. Over-
all, the spatial resolution of AF data can significantly affect the
interpretation of the underlying AF mechanism.
We thank Dr Hubert Cochet for the late gadolinium enhancement
(LGE)-magnetic resonance imaging data used in this study.
Sources of Funding
This work was supported by funding awarded from the British
Heart Foundation (FS/11/22/28745 and RG/16/3/32175); the
ElectroCardioMaths Programme of the Imperial BHF Centre of
Research Excellence; the National Institute for Health Research.
Dr Ng is funded by National Institute for Health Research Clinical
Lectureship (1716). Dr Roney is funded by a Lefoulon-Delalande
Foundation fellowship administered by the Institute of France. In
addition, this study was supported through the Investment of the
Future grant, ANR-10-IAHU-04, and the grant Equipex MUSIC
ANR-11-EQPX-0030. Computer time for this study was provided
by the computing facilities Mésocentre de Calcul Intensif Aquitain
of the Université de Bordeaux and of the Université de Pau et des
Pays de l’Adour.
by guest on May 17, 2017 from
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Ng SiongJennifer H. Tweedy, Prapa Kanagaratnam, Nicholas S. Peters, Edward J. Vigmond and Fu
Caroline H. Roney, Chris D. Cantwell, Jason D. Bayer, Norman A. Qureshi, Phang Boon Lim,
Spatial Resolution Requirements for Accurate Identification of Drivers of Atrial
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! !
Supplemental Material
Expanded Methods and Results
We initially determined resolution requirements for a regularly spaced two-
dimensional grid of data with homogeneous properties with a stable rotor or focal
source. We then tested these requirements on more complicated arrhythmias in a
bilayer model with spatially varying activation and repolarization properties, realistic
geometries and catheter electrode arrangements.
1.1 Simulations
1.1.1 Simulations: Generating a range of wavelengths
The wavelength of a sinusoidal wave is the wave speed v divided by the wave
frequency f. We assume the spatial wavelength in cardiac tissue varies linearly with
speed or frequency: λ =v/f.
The monodomain tissue model was used for excitation propagation in a 10cm x 10cm
two-dimensional sheet of tissue and the Courtemanche-Ramirez-Nattel human atrial
cell model 1 was used to represent transmembrane ionic currents. Electrical
remodelling in AF was incorporated by reducing the maximal ionic conductances of
Ito, IKur and ICaL by 50%, 50% and 70% respectively, following 2 .
Conduction velocity (CV) of the wavefront (wave speed) was modified using the
diffusion coefficient D. Three values of D were chosen (D=0.0005, 0.0010, 0.0015
cm2/ms) based on preliminary simulations that showed these values result in CVs that
span the physiological range in humans 3. Conductivities for homogeneous two-
dimensional sheet simulations were isotropic.
To modify the maximum frequency of propagation for simulated spiral waves, IK1
conductance was multiplied by 1.0, 1.5 or 2.0. Increasing this parameter has been
! !
shown to reduce the action potential duration (APD), and so increase the maximum
frequency of propagation, as well as to increase spiral wave stability in modelling
studies 4.
Spiral wave simulations were run for parameter set combinations of the three
diffusion coefficients with the three values of the IK1 conductance, resulting in nine
different wavelengths (see S-Table 1). This was repeated using the same parameter
sets for a focal source stimulus applied at a frequency close to the corresponding
spiral wave frequency (see S-Table 2). Initial conditions for each value of IK1
conductance and pacing frequency were obtained by prepacing a single cell for 100
beats in order to space clamp the 2D model with single cell conditions. In addition,
the sodium and potassium concentrations were treated as fixed constants to eliminate
drift, following 5 .
The monodomain equations were solved using a finite difference operator splitting
scheme in space 6 and an alternating-direction implicit scheme in time 7, with a space
step of 0.1mm and a time step of 0.01ms.
S-Table 1: Wavelengths for spiral wavefronts of rotor simulations (top lines: full
resolution calculated wavelengths (median and interquartile range); bottom lines:
estimated wavelength (CV x cycle length (CL))).
! !
S-Table 2: Wavelengths for circular wavefronts of focal source simulations (top
lines: full resolution calculated wavelengths (median and interquartile range); bottom
lines: estimated wavelength (CV x cycle length (CL))).
1.1.2 Simulations: Bilayer model
To test the effects of rotor stability and data type on resolution requirements,
simulations were run using a previously published atrial bilayer model 8. The finite
element model includes 2D endocardial and epicardial layers that are discretely
connected for the left atrium, as well as fast conducting pathways (Bachmann’s
bundle, crista terminalis, pectinate muscles). The Courtemanche AF cellular model
was used, tuned to match monophasic action potential duration of persistent AF
patients 9,10. Further rescalings were used to incorporate regional repolarisation
heterogeneity 9,11,12. Fiber orientation was included in the model following the rule
based approach of Labarthe et al. 13, and regional conductivity values were tuned to
match the activation data of Lemery et al 14. Simulations were run using the Cardiac
Arrhythmia Research Package (CARP) simulator 15.
These simulations included interstitial fibrosis as microstructural discontinuities in the
mesh 9,16, with distributions based on late-gadolinium intensity values for persistent
AF patients. In particular, edges were probabilistically selected as fibrotic based on
normalized LGE intensity and longitudinal fiber direction. Mesh element edges
parallel to the longitudinal fiber direction were taken to be four times more likely to
be fibrotic than edges that are transverse (using a scaling factor: α(4 cos2(θ) + sin2(θ)),
for which θ is the angle between a given edge and the longitudinal fiber direction for
the mesh element face). A uniformly distributed random number in the range (0,1)
was generated for each mesh element edge and compared to the product of the
normalised LGE intensity value and fiber direction scaling factor. Edges for which the
random number is less than this product were assigned to be fibrotic. These fibrotic
edges were arranged into connected networks so that no flux boundary conditions
could be applied, following Costa et al. 16. Mesh element faces for which all edges
were selected as fibrotic were removed from the mesh. For one of the simulations (Fig
4, main manuscript), we also modeled changes in tissue properties and cellular ionic
properties based on our previous publication 17.
! !
The LGE distribution used for the first simulation to test the effects of datatype were
for an individual patient with persistent AF; for the second simulation to compare
stable and meandering rotors, the distribution used is from Cochet et al. and
represents the likelihood of LGE intensity averaged across 26 patients with persistent
AF 18.
Unipolar electrograms were calculated at node locations projected 1mm endocardially
along the surface normal vectors; bipolar electrograms were calculated as the
difference of paired unipoles, with 4mm spacing, based on a PentaRay catheter
(BioSense Webster, South Diamond Bar, CA). Regional analysis was performed as in
our previous study 9, with the motivation that ablation strategies may target regions of
high PS density 19. For this analysis, the left atrium was divided into eight regions (see
Fig 1 of the main manuscript).
1.1.3 Simulations: Basket
The resolution requirements of a basket catheter were assessed by simulating a
realistic human left atrial geometry with unipolar electrograms calculated at basket
catheter measurement locations. The geometry was segmented (using ITK-SNAP 20)
from cardiac magnetic resonance imaging. The surface was opened at the four
pulmonary veins and at the mitral valve (using Blender 21), and re-meshed to create
triangular elements of characteristic size suitable for use with spectral/hp element
discretisations (using gmsh 22).
The locations of the electrodes of a basket catheter were exported from an electro-
anatomic mapping system used during a clinical case. This basket catheter was 48mm
in diameter and consisted of eight splines, with eight electrodes on each spline. The
electrode locations were shifted to be centred in the simulated atrial chamber and
rotated such that the largest gap between splines was located at the mitral valve. The
electrode locations were projected 0.2mm inside the blood cavity 23, along the surface
normal to the closest vertex.
! !
To establish the true location of rotors for comparison, unipolar electrograms were
calculated at every vertex of the mesh within the area covered by the basket catheter
and again projected 0.2mm inside the blood cavity (491 measurement points).
Simulations were run using the cardiac electrophysiology solver 24 in the Nektar++
spectral/hp element framework 25, with the Courtemanche-Ramirez-Nattel AF model
2. An extra-stimulus pacing protocol was employed to generate spiral wave re-entry in
the simulation. Unipolar electrograms were calculated at the electrode location points,
following 26. Phase of the unipolar electrograms were calculated as described
previously 17. After flattening to a two-dimensional representation 27,28, phase was
interpolated to a regular grid of 0.5mm spacing for identifying the true rotor location,
and 2mm spacing for the basket recording points. Interpolating the basket phase data
onto a finer grid than 2mm spacing caused wavefronts to artificially break-up.
Basket rotor locations were taken to be the closest PS location of the correct chirality
that was within a 10mm distance threshold of the high-resolution rotor location, on a
frame-by-frame basis. The moving-average rotor core path was estimated using a
window of length 1000ms that shifted in 100ms increments. For each window of data,
the width of the path (the diameter of the window) was calculated as the greatest
distance between the rotor core at any two times within that window.
1.2 Phase interpolation
To avoid the issue of interpolation across the phase angle branch cut, it was necessary
to convert the phase angle (θ) to exponential form (eiθ) before interpolation. The
mapped data was then interpolated, and finally converted back to phase angles
between -π and π. This is shown in Fig 1B of the main manuscript, comparing
interpolating θ (left) with mapping to eiθ, interpolating and then mapping back to θ
(right). Errors associated with the phase discontinuities in the direct interpolation
become significantly more pronounced as the resolution is reduced.
In order to assess the effects of spatial resolution on the observed wavefront
dynamics, the phase calculated using the downsampled data (resolutions ranging from
1mm to 25mm) were interpolated to the full grid resolution (0.1mm).
! !
The data were interpolated using the Matlab interp2 function, with spline
interpolation, since this resulted in the fewest number of false phase singularity
For low-resolution surface mesh data, an inverse distance squared weighting
interpolation was used (using neighbours within a 7mm radius sphere) 17. For the
atrial bilayer model, downsampled data of mesh resolution 1.62mm to 17.1mm (4813-
36 points) were interpolated to 1.62mm.
1.3 Using divergence to identify focal sources
For focal source identification, we calculated the divergence of the conduction
velocity field since peaks in divergence indicate locations of sources of electrical
activity 29. An outline of the steps involved is shown in S-Fig 1.
! !
S-Fig 1: Methodology for calculating divergence, used to identify focal sources from
activation time data. (A) Activation times for a simulated focal source; (B) times for
one focal beat downsampled to 2mm spacing; (C) normalised CV vectors; (D)
divergence of the CV field. The point of maximum divergence was used to identify
the origin of focal sources; seen clearly in (D). The CV vector field was normalised so
that the divergence depended only on direction, and not speed.
1.4 Wavelength Calculations
1.4.1 Estimating Wavelength
An automated algorithm to calculate the wavelength as the distance between arms of a
spiral wavefront or subsequent circular wavefronts of a focal source (Fig 3A, main
manuscript) works as follows. For each frame, an isopotential line was calculated (-
60mV) using the method from 30: points were selected for an isopotential line if and
only if, firstly, the potential of the node was less than the isopotential value and,
secondly, the values of between one and three of its four neighbouring nodes were
greater than the isopotential value. The isopotential line was split into regions of
positive and negative time derivatives. For spiral waves, the centre was defined as the
pixel where such gradients meet (!"
!" =0 and V(x,y,t)=-60) 31. Intersections of rays
from this centre with the isopotential line with positive gradient were located, and in
the instance where there was more than one intersection, the distance along the ray
between points was stored. This was repeated every 10 degrees and for frames every
10ms. The wavelength was taken to be the median of these distances.
For focal sources, the calculation was similar but the centre was the point of
maximum divergence.
1.4.2 Automated Conduction Velocity Analysis:
To correctly calculate conduction velocity for a given recording area, the time
window for the activation times analysed must be chosen appropriately such that the
activation times of each of the measuring points are from the same propagating
! !
For a spiral wave, this means the times should be from the same arm of the spiral; that
is between the same two turns of the wavefront. This is demonstrated in S-Fig 2 in
which the top row shows an inappropriate choice of times for which some points are
on one arm of the spiral and others on another, creating a discontinuity in the
activation time field; the bottom row shows an appropriate choice of times. The
conduction velocity is calculated correctly in the latter case. It can be challenging to
select the correct time window for analysis during complicated rhythms, such as
fibrillation, and so an automated method for selection is proposed here.
First of all, the median interval between subsequent activations of all measuring
points is calculated, to give an estimate of the average cycle length of the activity,
which is then used as the window length, L, for analysis. Activation times for each
recording point are then selected within a window starting at some initial start time, T,
giving [T, T+L] (in the instance that multiple activations occur within the window for
a recording location, the minimum time is selected). The conduction velocity is then
calculated for these times along with the residual of the fit. This is repeated for
intervals of length L, for which the start point is shifted from T, in 10ms increments,
until the end of the recording. The conduction velocity algorithm is applied to each
time window and those with a residual below a threshold value are selected as suitable
time windows, and the conduction velocity estimate is stored. In the example shown
in S-Fig 2, a shift equal to half of the median cycle length from the initial start time
gives the lowest residual and most appropriate choice of activation times.
For analysis of repeating wavefronts, including focal sources and spiral waves, this
technique was used in order to automatically find the conduction velocity, without the
need to pre-specify a time window. For the bilayer simulations, wavelength was
estimated on a downsampled mesh (average edge length 3.52mm). For each node of
this mesh, twenty nodes were selected within a 1cm radius of the node (to
approximate recordings on a high-density catheter), activation times were defined as
the timings of phase 0 for action potential phase, and the mean and standard deviation
conduction velocity estimate was calculated as described above. The wavelength was
then estimated for each node as the mean conduction velocity multiplied by the mean
cycle length at that point. Finally this score was smoothed using an inverse distance
! !
S-Fig 2: Calculation of the conduction velocity of a spiral wavefront. (A, D):
Activation times were analysed for the points shown at the purple dots in the
isochronal maps. (B, E): Locations of the points used for the fit, coloured by their
activation times. (C, F): Plots to show the actual times and fitted times that result from
using these points in the conduction velocity algorithm assuming a circular wavefront.
(A-C) A poor fit is obtained when activation times are not on the same arm of a spiral,
as the first and last measuring points to be activated are both in the centre of the
arrangement of points. (D-F) Shifting by the median cycle length divided by two
gives a time window for which the times are all on the same arm of the spiral, and a
satisfactory fit is obtained. In this case, the first points to be activated are in the
bottom left of the arrangement, and the last points to be activated are in the top right.
The domain size shown here is 10cm x 10cm.
! !
! !
2. 1 Estimating wavelength
A range of wavelengths was simulated for spiral wavefronts and circular wavefronts
using combinations of the diffusion co-efficient D and potassium conductance gK1 as
described in Supplemental Material section 1.1.1. Spiral wavefront wavelengths were
within the range 33.6-78.3mm (S-Table 1), while circular wavefront wavelengths
covered the range 32.0-62.5mm (S-Table 2). For focal activation (circular
wavefronts), three out of nine of the simulated parameter combinations produced
wavelengths which were too large (>70mm) to be measured within the computational
domain, which was chosen based on a typical left-atrial surface area (100cm2).
Wavelengths estimated using limited-resolution data, as the product of CV and cycle
length (CL), matched the calculated wavelength to within an average percentage error
of 3.3% for spiral waves and 1.4% for focal activations, as given in S-Tables 1 and 2,
respectively. This was based on a random distribution of twenty points within an area
of diameter 2cm, approximating a high-density multipolar catheter.
The number of measuring points required for successful estimation of rotor or focal
source wavelengths was found to be between six and seven. For spiral waves at the
shortest wavelengths (33.6mm), seven points were required (20.0% of CV estimates
unsuccessful for 6 points; 2.5% unsuccessful for 7 points). For the longest wavelength
spiral wave simulation (78.3mm), six points were required (10.0% of CV estimates
unsuccessful for 5 points; 0% unsuccessful for 6 points).
For focal sources (circular wavefronts), resolution requirements were found to be
similar to those for rotors (spiral wavefronts). Seven points were required for a
wavelength of 53.2mm (12.5% of CV estimates unsuccessful for 6 points; 7.5%
unsuccessful for 7 points).
2.2 Using divergence to identify focal sources
! !
In order for focal source identification using the maximum divergence to be
successful, there must be a 3x3 grid of measuring points between consecutive
wavefronts. This is illustrated in S-Fig 3.
S-Fig 3: Resolution requirements for focal source identification depend on spatial
wavelength. Having three by three points within a single focal source circular
wavefront gives the minimum information required for successful identification of the
maximum divergence location. A denser grid is required for shorter wavelengths. A-C
are for a shorter wavelength of 32mm, for which a resolution spacing of 20mm or
smaller is required to give three grid points; while D-F are for a longer wavelength of
63mm, for which a minimum resolution spacing of 41mm is required. A, D show
isochronal maps; B, E show the times used for the stated resolutions; C, F show the
interpolated velocity fields from which the point of maximum divergence is located.
2.3 Basket path
S-Fig 4 shows that the path followed by the meandering rotor core estimated using the
basket arrangement is visually similar to the path measured using the dense
! !
arrangement. The average frame-wise error in the rotor core path is 2.2 ± 1.2mm for
the first rotor and 3.8 ± 2.1mm for the second rotor. The average path is therefore
accurate; however, the PS trajectory shows a larger rotor meander area for the basket
resolution data than for the high-resolution data (diameter increased for basket
compared to high resolution by 8.7 ± 3.5mm and 3.4 ± 7.0mm respectively for each
S-Fig 4: Moving average PS path for the basket catheter arrangement. PS locations
for thirty seconds of the longer wavelength simulation (75.2mm) are shown. PSs are
separated by chirality (top and bottom row) to show the locations of the two rotors,
for the high-resolution data and 8-spline basket catheter arrangement. Location of the
moving average core location is marked in black.
! !
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Supplementary resource (1)

... However, ablation therapy based on rotor identification has limited success, partially due to inconsistent results with respect to rotor identification sites. It was also demonstrated in Roney et al. [86] that spatial resolution is essential in identifying the core of the rotors. Sequential mapping catheters have higher resolution than basket catheters but also have smaller spatial area coverage. ...
... Several studies demonstrated successful AF driver identification by phase mapping of simultaneous recordings using a basket catheter [9] and a noninvasive array of body surface electrodes [90]. It was also demonstrated in Roney et al. [86] that spatial resolution is essential in identifying the AF reentrant activity. ...
... After applying the Hilbert transform, the instantaneous phase was interpolated using complex vector interpolation to avoid incorrect phase calculation. 37,38 Further details about the phase reconstruction is provided in supplementary material S3a. ...
... A number of studies question the efficacy of basket catheter recordings in the study of electrophysiological properties of fibrillation due to technical limitations such as electrode spacing and insufficient contact with the tissue. 38 We acknowledge that these concerns, however by examining human VF recorded using a 256electrode sock that holistically examined epicardial VF, along with computational simulations of fibrillatory behavior, we show that the same trends occur in other systems and are not a consequence the basket catheter limitations nor are the findings obscured by them. ...
Atrial and ventricular fibrillation (AF/VF) are characterized by the repetitive regeneration of topological defects known as phase singularities (PSs). The effect of PS interactions has not been previously studied in human AF and VF. We hypothesized that PS population size would influence the rate of PS formation and destruction in human AF and VF, due to increased inter-defect interaction. PS population statistics were studied in computational simulations (Aliev-Panfilov), human AF and human VF. The influence of inter-PS interactions was evaluated by comparison between directly modeled discrete-time Markov chain (DTMC) transition matrices of the PS population changes, and M/M/∞ birth-death transition matrices of PS dynamics, which assumes that PS formations and destructions are effectively statistically independent events. Across all systems examined, PS population changes differed from those expected with M/M/∞. In human AF and VF, the formation rates decreased slightly with PS population when modeled with the DTMC, compared with the static formation rate expected through M/M/∞, suggesting new formations were being inhibited. In human AF and VF, the destruction rates increased with PS population for both models, with the DTMC rate increase exceeding the M/M/∞ estimates, indicating that PS were being destroyed faster as the PS population grew. In human AF and VF, the change in PS formation and destruction rates as the population increased differed between the two models. This indicates that the presence of additional PS influenced the likelihood of new PS formation and destruction, consistent with the notion of self-inhibitory inter-PS interactions.
... Detection of RAAPs necessitates simultaneous, high-resolution recordings of the entire heart chamber, a challenging task due to the limitations of catheter technology [15]. While high-density contact mapping catheters offer a sufficient electrode density for mapping drivers, their spatial coverage is limited [16]. Panoramic mapping techniques have been developed to improve coverage, particularly for rotating patterns [17,18]. ...
... Panoramic mapping techniques have been developed to improve coverage, particularly for rotating patterns [17,18]. However, these methods have limited spatial resolution, resulting in low sensitivity and specificity in reentry detection [16,19]. To date, the trade-off between high-density and high-coverage remains a challenge. ...
Background: Repetitive atrial activation patterns (RAAPs) during atrial fibrillation (AF) may be associated with localized mechanisms that maintain AF. Current electro-anatomical mapping systems are unsuitable for analyzing RAAPs due to the trade-off between spatial coverage and electrode density in clinical catheters. This work proposes a technique to overcome this trade-off by constructing composite maps from spatially overlapping sequential recordings. Methods: High-density epicardial contact mapping was performed during open-chest surgery in goats (n=16, left and right atria) with 3 or 22 weeks of sustained AF (249-electrode array, electrode distance 2.4 mm). A dataset mimicking sequential recordings was generated by segmenting the grid into four spatially overlapping regions (each region 6.5 cm2, 48±10% overlap) without temporal overlap. RAAPs were detected in each region using recurrence plots of activation times. RAAPs in two different regions were joined in case of RAAP cross-recurrence between overlapping electrodes. We quantified the reconstruction success rate and quality of the composite maps. Results: Of 1021 RAAPs found in the full mapping array (32±13 per recording), 328 spatiotemporally stable RAAPs were analyzed. 247 composite maps were generated (75% success) with a quality of 0.86±0.21 (Pearson correlation). Success was significantly affected by the RAAP area. Quality was weakly correlated with the number of repetitions of RAAPs (r=0.13, p<0.05) and not affected by the atrial side (left or right) or AF duration (3 or 22 weeks of AF). Conclusions: Constructing composite maps by combining spatially overlapping sequential recordings is feasible. Interpretation of these maps can play a central role in ablation planning.
... However, ablation strategies focused on targets suggested by such approaches still did not lead to better therapy outcomes [1]. These results may be related to technical limitations, such as low coverage or spatial resolution of existing mapping catheters [4], or to the fact that they do not reflect precisely the locations of driving mechanisms [5]. ...
... Mapping of AF and localization of eventual driving mechanisms is limited either by the spatial resolution or coverage of the employed catheters. While panoramic mapping catheters may give a better overview of the activation patterns, their lower spatial resolution may lead to false positive detection of drivers, with lower localization precision [4]. Sequential high-density mapping strategies are, on the other hand, limited by the field of view of the catheters, but provide better spatial resolution to determine the regions that may sustain driving mechanisms. ...
... Subsequently, FA is quantitatively detected using numerical methods, such as spatial gradient and divergence analysis, or the directed graph analysis of the activation map. However, it is known that the conduction velocity (CV) vector field calculated using the activation map is discontinuous near the wavefront (WF) [14]. It is therefore expected that numerous false positives will result from applying this method to complex and aperiodic excitation during cardiac fibrillation, where multiple WFs occur simultaneously. ...
Full-text available
Purpose Atrial fibrillation is the most common arrhythmia. Spiral wave and focal activation (FA) are known to play an important mechanistic role in the generation, sustenance, and termination of tachyarrhythmia. However, to date no quantitative method of detecting FA under complex excitations has yet been established. Methods In this study, we propose such a detection method of FA by calculating the divergence of the spatial gradient of a phase map, which identifies the phase of the excitation cycle at each point of the heart as derived from measurement signals. Next, to verify the accuracy of the proposed method, we conducted a membrane potential measurement experiment using an excised porcine heart ( n = 1). Results By comparing the conventional and proposed methods for 126 instances of FA, we found that the proposed method showed improved detection accuracy, with precision, sensitivity, and F-measure values of 0.45, 0.84, and 0.58, while conventional method showed 0.04, 0.26, and 0.08, respectively. Conclusion The proposed method, which uses the divergence of the phase gradient to predict FA, shows potential to suppress false positives that are observed in the conventional method, and it can more accurately detect FA than conventional methods.
... 40 The flaws seen with inter-spline bunching resulted in a loss of coverage and contact, 41 and only 63.1% of the inter-electrode distances were less than the most stringent spatial resolution required for the identification of rotors in human AF. Moreover, a computer simulation study 42 found that several high-density mapping catheters (AFocusII and PentaRay) had interelectrode spacings below minimum resolution (11.9 mm), suggesting that these catheters have a higher resolution to locate PSs if placed over the rotor core accurately. Although these catheters have satisfactory mapping resolution, they are not panoramic mapping devices that could show overall atrial electrical activity. ...
Full-text available
Treatment of atrial fibrillation (AF) remains challenging despite significant progress in understanding its underlying mechanisms. The first detailed, quantitative theory of functional re-entry, the 'leading circle' model, was developed more than 40 years ago. Subsequently, in decades of study, an alternative paradigm based on spiral waves has long been postulated to drive AF. The rotor as a 'spiral wave generator' is a curved 'vortex' formed by spin motion in the two-dimensional plane, identified using advanced mapping methods in experimental and clinical AF. However, it is challenging to achieve complementary results between experimental results and clinical studies due to the limitation in research methods and the complexity of the rotor mechanism. Here, we review knowledge garnered over decades on generation, electrophysiological properties, and three-dimensional (3D) structure diversity of the rotor mechanism and make a comparison among recent clinical approaches to identify rotors. Although initial studies of rotor ablation at many independent centres have achieved promising results, some inconclusive outcomes exist in others. We propose that the clinical rotor identification might be substantially influenced by (i) non-identical surface activation patterns, which resulted from a diverse 3D form of scroll wave, and (ii) inadequate resolution of mapping techniques. With rapidly advancing theoretical and technological developments, future work is required to resolve clinically relevant limitations in current basic and clinical research methodology, translate from one to the other, and resolve available mapping techniques.
Full-text available
There are a variety of difficulties in evaluating clinical cardiac mapping systems, most notably the inability to record the transmembrane potential throughout the entire heart during patient procedures which prevents the comparison to a relevant “gold standard”. Cardiac mapping systems are comprised of hardware and software elements including sophisticated mathematical algorithms, both of which continue to undergo rapid innovation. The purpose of this study is to develop a computational modeling framework to evaluate the performance of cardiac mapping systems. The framework enables rigorous evaluation of a mapping system’s ability to localize and characterize (i.e., focal or reentrant) arrhythmogenic sources in the heart. The main component of our tool is a library of computer simulations of various dynamic patterns throughout the entire heart in which the type and location of the arrhythmogenic sources are known. Our framework allows for performance evaluation for various electrode configurations, heart geometries, arrhythmias, and electrogram noise levels and involves blind comparison of mapping systems against a “silver standard” comprised of computer simulations in which the precise transmembrane potential patterns throughout the heart are known. A feasibility study was performed using simulations of patterns in the human left atria and three hypothetical virtual catheter electrode arrays. Activation times (AcT) and patterns (AcP) were computed for three virtual electrode arrays: two basket arrays with good and poor contact and one high-resolution grid with uniform spacing. The average root mean squared difference of AcTs of electrograms and those of the nearest endocardial action potential was less than 1 ms and therefore appears to be a poor performance metric. In an effort to standardize performance evaluation of mapping systems a novel performance metric is introduced based on the number of AcPs identified correctly and those considered spurious as well as misclassifications of arrhythmia type; spatial and temporal localization accuracy of correctly identified patterns was also quantified. This approach provides a rigorous quantitative analysis of cardiac mapping system performance. Proof of concept of this computational evaluation framework suggests that it could help safeguard that mapping systems perform as expected as well as provide estimates of system accuracy.
Full-text available
Heart rhythm disorders, known as arrhythmias, cause significant morbidity and are one of the leading causes of mortality. Cardiac arrhythmias are frequently treated by implantable devices, such as pacemakers and defibrillators, or by ablation therapy guided by electroanatomical mapping. Both implantable and ablation therapies require sophisticated biointerfaces for electrophysiological measurements of electrograms and delivery of therapeutic stimulation or ablation energy. In this work, we report for the first time on graphene biointerface for in vivo cardiac electrophysiology. Leveraging sub-micrometer thick tissue-conformable graphene arrays, we demonstrate sensing and stimulation of the open mammalian heart both in vitro and in vivo. Furthermore, we demonstrate the graphene biointerface treatment of atrioventricular block (the kind of arrhythmia where the electrical conduction from the atria to the ventricles is interrupted). The graphene arrays show effective electrochemical properties, namely interface impedance down to 40 Ohm×cm2 at 1 kHz, charge storage capacity up to 63.7 mC/cm2 , and charge injection capacity up to 704 μC/cm2 . Transparency of the graphene structures allows for simultaneous optical mapping of cardiac action potentials, calcium transients, and optogenetic stimulation while performing electrical measurements and stimulation. Our report presents evidence of the significant potential of graphene biointerfaces for advanced cardiac electrophysiology and arrhythmia therapy. This article is protected by copyright. All rights reserved.
Background: Dominant frequencies (DFs) or complex fractionated atrial electrograms (CFAEs), indicative of focal sources or rotational activation, are used to identify target sites for atrial fibrillation (AF) ablation in clinical studies, although the relationship among DF, CFAE, and activation patterns remains unclear. Objectives: This study sought to investigate the relationship between patterns of activation underlying DF and CFAE sites during AF. Methods: Epicardial high-resolution mapping of the right and left atrium including Bachmann's bundle was performed in 71 participants. We identified the highest dominant frequency (DFmax) and highest degree of CFAE (CFAEmax) with the use of existing clinical criteria and classified patterns of activation as focal or rotational activation and smooth propagation, conduction block (CB), collision and remnant activity, and fibrillation potentials as single, double, or fractionated potentials containing, respectively, 1, 2, or 3 or more negative deflections. Relationships among activation patterns, DFmax, and potential types were investigated. Results: DFmax were primarily located at the left atrioventricular groove and did not harbor focal activation (proportion focal waves: 0% [IQR: 0%-2%]). Compared with non-DFmax sites, DFmax were characterized by more frequent smooth propagation (22% [IQR: 7%-48%] vs 17% [IQR: 11%-24%]; P = 0.001), less frequent conduction block (69% [IQR: 51%-81%] vs 74% [IQR: 69%-78%]; P = 0.006), a higher proportion of single potentials (72% [IQR: 55%-84%] vs 6%1 [IQR: 55%-65%]; P = 0.003), and a lower proportion of fractionated potentials (4% [IQR: 1%-11%] vs 12% [IQR: 9%-15%]; P = 0.004). CFAEmax were mainly found at the pulmonary veins area, and only 1% [IQR: 0%-2%] of all CFAEmax contained focal activation. Compared with non-CFAEmax sites, CFAEmax sites were characterized by less frequent smooth propagation (1% [IQR: 0%-1%] vs 17% [IQR: 12%-24%]; P < 0.001) and more frequent remnant activity (20% [IQR: 12%-29%] vs 8% [IQR: 5%-10%]; P < 0.001), and harbored predominantly fractionated potentials (52% [IQR: 43%-66%] vs 12% [IQR: 9%-14%]; P < 0.001). Conclusions: Focal or rotational patterns of activation were not consistently detected at DFmax domains and CFAEmax sites. These findings do not support the concept of targeting DFmax or CFAEmax according to existing criteria for AF ablation.
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Aims: Catheter ablation is an effective technique for terminating atrial arrhythmia. However, given a high atrial fibrillation (AF) recurrence rate, optimal ablation strategies have yet to be defined. Computer modelling can be a powerful aid but modelling of fibrosis, a major factor associated with AF, is an open question. Several groups have proposed methodologies based on imaging data, but no comparison to determine which methodology best corroborates clinically observed reentrant behaviour has been performed. We examined several methodologies to determine the best method for capturing fibrillation dynamics. Methods and results: Patient late gadolinium-enhanced magnetic resonance imaging data were transferred onto a bilayer atrial computer model and used to assign fibrosis distributions. Fibrosis was modelled as conduction disturbances (lower conductivity, edge splitting, or percolation), transforming growth factor-β1 ionic channel effects, myocyte-fibroblast coupling, and combinations of the preceding. Reentry was induced through pulmonary vein ectopy and the ensuing rotor dynamics characterized. Non-invasive electrocardiographic imaging data of the patients in AF was used for comparison. Electrograms were computed and the fractionation durations measured over the surface. Edge splitting produced more phase singularities from wavebreaks than the other representations. The number of phase singularities seen with percolation was closer to the clinical values. Addition of fibroblast coupling had an organizing effect on rotor dynamics. Simple tissue conductivity changes with ionic changes localized rotors over fibrosis which was not observed with clinical data. Conclusion: The specific representation of fibrosis has a large effect on rotor dynamics and needs to be carefully considered for patient specific modelling.
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Extracellular electrograms recorded during atrial fibrillation (AF) are challenging to interpret due to the inherent beat-to-beat variability in amplitude and duration. Phase mapping represents these voltage signals in terms of relative position within the cycle, and has been widely applied to action potential and unipolar electrogram data of myocardial fibrillation. To date, however, it has not been applied to bipolar recordings, which are commonly acquired clinically. The purpose of this study is to present a novel algorithm for calculating phase from both unipolar and bipolar electrograms recorded during AF. A sequence of signal filters and processing steps are used to calculate phase from simulated, experimental, and clinical, unipolar and bipolar electrograms. The algorithm is validated against action potential phase using simulated data (trajectory centre error <0.8 mm); between experimental multi-electrode array unipolar and bipolar phase; and for wavefront identification in clinical atrial tachycardia. For clinical AF, similar rotational content (R² = 0.79) and propagation maps (median correlation 0.73) were measured using either unipolar or bipolar recordings. The algorithm is robust, uses standard signal processing techniques, and accurately quantifies AF wavefronts and sources. Identifying critical sources, such as rotors, in AF, may allow for more accurate targeting of ablation therapy and improved patient outcomes. Electronic supplementary material The online version of this article (doi:10.1007/s10439-016-1766-4) contains supplementary material, which is available to authorized users.
Conference Paper
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Electro-anatomic mapping and medical imaging systems, used during clinical procedures for treatment of atrial arrhythmias, frequently record and display measurements on an anatomical surface of the left atrium. As such, obtaining a complete picture of activation necessitates simultaneous views from multiple angles. In addition, post-processing of three-dimensional surface data is challenging, since algorithms are typically applicable to planar or volumetric data. We applied a surface flattening methodology to medical imaging data and electro-anatomic mapping data to generate a two-dimensional representation that best preserves distances, since the calculation of many clinically relevant metrics, including conduction velocity and rotor trajectory identification require an accurate representation of distance. Distance distortions were small and improved upon exclusion of the pulmonary veins. The technique is demonstrated using maps of local activation time, based on clinical data, and plotting rotor-core trajectories, using simulated data.
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Pulmonary vein isolation (PVI) with radiofrequency ablation (RFA) is the cornerstone of atrial fibrillation (AF) therapy, but few strategies exist for when it fails. To guide RFA, phase singularity (PS) mapping locates reentrant electrical waves (rotors) that perpetuate AF. The goal of this study was to test existing and develop new RFA strategies for terminating rotors identified with PS mapping. It is unsafe to test experimental RFA strategies in patients, so they were evaluated in silico using a bilayer computer model of the human atria with persistent AF (pAF) electrical (ionic) and structural (fibrosis) remodeling. pAF was initiated by rapidly pacing the right (RSPV) and left (LSPV) superior pulmonary veins during sinus rhythm, and rotor dynamics quantified by PS analysis. Three RFA strategies were studied: (i) PVI, roof, and mitral lines; (ii) circles, perforated circles, lines, and crosses 0.5-1.5 cm in diameter/length administered near rotor locations/pathways identified by PS mapping; and (iii) 4-8 lines streamlining the sequence of electrical activation during sinus rhythm. As in pAF patients, 2 ± 1 rotors with cycle length 185 ± 4 ms and short PS duration 452 ± 401 ms perpetuated simulated pAF. Spatially, PS density had weak to moderate positive correlations with fibrosis density (RSPV: r = 0.38, p = 0.35, LSPV: r = 0.77, p = 0.02). RFA PVI, mitral, and roof lines failed to terminate pAF, but RFA perforated circles and lines 1.5 cm in diameter/length terminated meandering rotors from RSPV pacing when placed at locations with high PS density. Similarly, RFA circles, perforated circles, and crosses 1.5 cm in diameter/length terminated stationary rotors from LSPV pacing. The most effective strategy for terminating pAF was to streamline the sequence of activation during sinus rhythm with >4 RFA lines. These results demonstrate that co-localizing 1.5 cm RFA lesions with locations of high PS density is a promising strategy for terminating pAF rotors. For patients immune to PVI, roof, mitral, and PS guided RFA strategies, streamlining patient-specific activation sequences during sinus rhythm is a robust but challenging alternative.
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Objectives: This study sought to evaluate basket catheter deployment, catheter-tissue contact, and time-space stability of unipolar atrial electrograms (aEGMs) recorded in persistent atrial fibrillation (AF) patients. Background: Panoramic mapping of human AF using multiple-electrode basket catheters may identify AF sources. Although clinical results using this technique are provocative, questions remain about its effectiveness. Methods: Data were collected from patients (N = 25) undergoing catheter ablation for AF during the multicenter STARLIGHT (Signal Transfer of Atrial Fibrillation Data to Guide Human Treatment) trial (NCT01765075). Left and right aEGM signals were recorded using basket catheters during baseline AF, following ablation and during sinus rhythm. Data were analyzed for basket deployment, peak-to-peak voltage, and electrogram stability and organization. Electrogram stability and organization were evaluated via time-frequency analysis (TFA). Results: Basket catheters displayed equatorial bunching when deployed in atria. Interspline spacing ranged from 1.7 to 64.0 mm in the right atrial and from 1.5 to 85.08 mm in the left atrial basket. Approximately one-third of mapping electrodes failed to demonstrate a median peak-to-peak voltage >2× the low-voltage threshold. Time-space stability and organization was observed in 13 of 22 (59.09%) right atrial and 10 of 22 (45.45%) left atrial baskets. Conclusions: Despite poor deployment and a large number of low-voltage electrodes, stability and organization was observed in about one-half of the mapped patients. Although this study suggests that basket catheters have limitations for patient-specific AF mapping, concordant activation occurs in some persistent AF patients, which may be amenable to high-density mapping techniques.
Background: The activation pattern of localized reentry (LR) in atrial tachycardia remains incompletely understood. We used the ultra-high density Rhythmia mapping system to study activation patterns in LR. Methods and results: LR was suggested by small rotatory activations (carousels) containing the full spectrum of the color-coded map. Twenty-three left-sided atrial tachycardias were mapped in 15 patients (age: 64±11 years). 16 253±9192 points were displayed per map, collected over 26±14 minutes. A total of 50 carousels were identified (median 2; quartiles 1-3 per map), although this represented LR in only n=7 out of 50 (14%): here, rotation occurred around a small area of scar (<0.03 mV; 12±6 mm diameter). In LR, electrograms along the carousel encompassed the full tachycardia cycle length, and surrounding activation moved away from the carousel in all directions. Ablating fractionated electrograms (117±18 ms; 44±13% of tachycardia cycle length) within the carousel interrupted the tachycardia in every LR case. All remaining carousels were pseudo-reentrant (n=43/50 [86%]) occurring in areas of wavefront collision (n=21; median 0.5; quartiles 0-2 per map) or as artifact because of annotation of noise or interpolation in areas of incomplete mapping (n=22; median 1, quartiles 0-2 per map). Pseudo-reentrant carousels were incorrectly ablated in 5 cases having been misinterpreted as LR. Conclusions: The activation pattern of LR is of small stable rotational activations (carousels), and this drove 30% (7/23) of our postablation atrial tachycardias. However, this appearance is most often pseudo-reentrant and must be differentiated by interpretation of electrograms in the candidate circuit and activation in the wider surrounding region.
We have considered the propagation of excitation in a plane medium inhomogeneous in refractoriness. It has been shown that a state of activity resembling fibrillation is possible. This state appears if the medium is supplied with several pulses following at high frequencies. Closed pathways of conduction are formed-reverberators, which for the medium are foci of automatic activity. Reverberators operating at different frequencies are not synchronized. The high frequency of impulsation appearing on their interaction in a medium may lead to the appearance of new reverberators. Each reverberator lives only a finite time-longer the more homogeneous the adjacent areas of the medium. In a medium of sufficient dimensions "dying" of some reverberators and the appearance of others constantly occurs. If excitation is not instantaneous, then the perimeter of the reverberator may be less than the Wiener wavelength-product of the refractoriness and the velocity. The requirements fall for the dimensions of the medium in which "fibrillation" is possible.
Background: New approaches to ablation of atrial fibrillation (AF) include focal impulse and rotor modulation (FIRM); studies of this technology with short-term follow-up have shown favorable outcomes. Objective: We sought to characterize the long-term results of FIRM ablation in a cohort of patients treated at two academic medical centers. Methods: All FIRM-guided ablation procedures (n=43) at UCLA Medical Center and Virginia Commonwealth University Medical Center performed between 1/2012 and 10/2013 were included for analysis. During AF, FIRM software constructed phase maps from unipolar atrial electrograms to identify putative AF sources. These sites were targeted for ablation, along with pulmonary vein isolation (PVI) in 77% of patients. Results: AF was paroxysmal in 56%, and 67% had prior AF ablation. All patients had rotors identified (mean 2.6±1.2 per patient, 77% in LA). Pre-specified acute procedural endpoint was achieved in 47% of patients (n=20): AF termination (n=4), organization (n=7), or >10% slowing of AF cycle length (n=9). Acute complications occurred in 4 patients (9.3%). At 18±7 months of follow-up, 37% were free from documented recurrent AF after a 3-month blanking period; 21% were free from documented atrial tachyarrhythmias and off antiarrhythmic drugs. Multivariate analysis did not reveal any significant predictors of AF recurrence, including pattern of AF, acute procedural success, or prior failed ablation. Conclusions: Long-term clinical results after FIRM ablation in this cohort of patients showed poor efficacy, different from previously published studies. Randomized studies are needed to evaluate the efficacy and clinical utility of this ablation approach for treating AF.
Background: -The mechanism(s) of persistent and long-standing persistent (LSP) atrial fibrillation (AF) is/are poorly understood. We performed high density, simultaneous, bi-atrial, epicardial mapping of persistent and LSP AF in patients undergoing open heart surgery (OHS) 1) to test the hypothesis that persistent and LSP AF are due to one or more drivers, either focal or reentrant, and 2) to characterize associated atrial activation. Methods and results: -Twelve patients with persistent and LSP AF (1 month - 9 years duration) were studied at OHS. During AF, electrograms (AEGs) were recorded from both atria simultaneously for 1-5 minutes from 510-512 epicardial electrodes with ECG lead II. Thirty-two consecutive seconds of activation sequence maps were produced per patient. During AF, multiple foci (QS unipolar AEGs) of different cycle lengths (mean 175±18 ms) were present in both atria in 11/12 patients. Foci (2-4 per patient, duration 5-32 secs) were either sustained or intermittent, were predominantly found in the lateral left atrial free wall, and likely acted as drivers. Random and nonrandom breakthrough activation sites (initial r or R in unipolar AEGs) were also found. In 1/12 patients, only breakthrough sites were found. All wave fronts emanated from foci and/or breakthrough sites, and largely either collided or merged with each other at variable sites. Repetitive focal QS activation occasionally generated repetitive wannabe reentrant activation in 5/12 patients. No actual reentry was found. Conclusions: -During persistent and LSP AF in 12 patients, wave fronts emanating from foci and/or breakthrough sites maintained AF. No reentry was demonstrated.
-New approaches to ablation of atrial fibrillation (AF) include focal impulse and rotor modulation (FIRM) mapping, and initial results reported with this technique have been favorable. We sought to independently evaluate the approach by analyzing quantitative characteristics of atrial electrograms (AEGMs) used to identify rotors, and describe acute procedural outcomes of FIRM-guided ablation. -All FIRM-guided ablation procedures (n=24, 50% paroxysmal) at UCLA Medical Center were included for analysis. During AF, unipolar AEGMs collected from a 64-pole basket catheter were used to construct phase maps and identify putative AF sources. These sites were targeted for ablation, in conjunction with pulmonary vein isolation (PVI) in most patients (n=19, 79%). All patients had rotors identified (mean 2.3 ± 0.9 per patient, 72% in LA). Prespecified acute procedural endpoint was achieved in 12/24 (50%) patients: AF termination (n=1), organization (n=3), or >10% slowing of AF cycle length (n=8). Basket electrodes were within 1cm of 54% of LA surface area, and a mean of 31 electrodes per patient showed interpretable AEGMs. Offline analysis revealed no differences between rotor and distant sites in dominant frequency or Shannon entropy. Electroanatomic mapping showed no rotational activation at FIRM-identified rotor sites in 23/24 patients (96%). -FIRM-identified rotor sites did not exhibit quantitative AEGM characteristics expected from rotors, and did not differ quantitatively from surrounding tissue. Catheter ablation of these sites, in conjunction with PVI, resulted in AF termination or organization in a minority of patients (4/24, 17%). Further validation of this approach is necessary.