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Jolijn M Lubrecht, Thomas Grandits, Ali Gharaviri, Ulrich Schotten, Thomas Pock, Gernot Plank, Rolf Krause, Angelo Auricchio, Giulio Conte, Simone Pezzuto, Automatic reconstruction of the left atrium activation from sparse intracardiac contact recordings by inverse estimate of fibre structure and anisotropic conduction in a patient-specific model, EP Europace, Volume 23, Issue Supplement_1, March 2021, Pages i63–i70, https://doi.org/10.1093/europace/euaa392
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Abstract
Electric conduction in the atria is direction-dependent, being faster in fibre direction, and possibly heterogeneous due to structural remodelling. Intracardiac recordings of atrial activation may convey such information, but only with high-quality data. The aim of this study was to apply a patient-specific approach to enable such assessment even when data are scarce, noisy, and incomplete.
Contact intracardiac recordings in the left atrium from nine patients who underwent ablation therapy were collected before pulmonary veins isolation and retrospectively included in the study. The Personalized Inverse Eikonal Model from cardiac Electro-Anatomical Maps (PIEMAP), previously developed, has been used to reconstruct the conductivity tensor from sparse recordings of the activation. Regional fibre direction and conduction velocity were estimated from the fitted conductivity tensor and extensively cross-validated by clustered and sparse data removal. Electrical conductivity was successfully reconstructed in all patients. Cross-validation with respect to the measurements was excellent in seven patients (Pearson correlation r > 0.93) and modest in two patients (r = 0.62 and r = 0.74). Bland–Altman analysis showed a neglectable bias with respect to the measurements and the limit-of-agreement at –22.2 and 23.0 ms. Conduction velocity in the fibre direction was 82 ± 25 cm/s, whereas cross-fibre velocity was 46 ± 7 cm/s. Anisotropic ratio was 1.91±0.16. No significant inter-patient variability was observed. Personalized Inverse Eikonal model from cardiac Electro-Anatomical Maps correctly predicted activation times in late regions in all patients (r = 0.88) and was robust to a sparser dataset (r = 0.95).
Personalized Inverse Eikonal model from cardiac Electro-Anatomical Maps offers a novel approach to extrapolate the activation in unmapped regions and to assess conduction properties of the atria. It could be seamlessly integrated into existing electro-anatomic mapping systems. Personalized Inverse Eikonal model from cardiac Electro-Anatomical Maps also enables personalization of cardiac electrophysiology models.
Model-based extrapolation of activation map in specific regions even in the absence of mapping data.
Global consistency of activation maps and conductivity tensor to allow patient-specific modelling.
Assessment of local fibre direction from a single intracardiac recording using inverse modelling in nine patients undergoing to ablation therapy.
Estimate of the anisotropic conduction velocity, along and orthogonal to the fibres.
Methodology uniquely based on catheter mapping data, therefore readily embeddable into existing mapping systems.
Introduction
The quantitative assessment of the electrical substrate in the atria is essential for understanding the onset and perpetuation of atrial fibrillation (AF). Personalized therapeutic approaches for optimal ablation treatment, such as those based on computer modelling, heavily rely on the localization of scars and the regional distribution of fibrosis.1 Such regions, clinically identified through the permeability of contrast agents during cardiac imaging, are associated with a significant reduction in conduction velocity (CV) and could therefore constitute the ideal substrate for re-entrant arrhythmia.2 Moreover, CV in the atria is anisotropic due to the presence of fibres, and the anisotropic ratio, usually around 3:1,3 may be significantly altered by structural remodelling such as endomysial fibrosis, hence increasing the complexity of AF.4
High-density intracardiac contact recordings, with their unprecedented spatial and temporal resolution, are the ideal candidate for evaluating the local conduction properties. The high resolution enables sophisticated approaches to compute the CV.5,6 While being computationally efficient and easy to implement, these methods heavily rely on the quality and coverage of the map, which is often time-consuming to acquire. Moreover, they only provide front velocity rather than the actual conductivity of the tissue. Breakthroughs and front collisions may also distort the CV. Thus, the estimated CV may not allow for correct estimation of atrial conductivity of the atria.
We recently proposed a novel approach, called Personalized Inverse Eikonal Model from cardiac Electro-Anatomical Maps (PIEMAP), to estimate the anisotropic conduction from high-density electro-anatomical maps (EAMs) which also overcomes several of the above drawbacks of classic methods.7 Personalized Inverse Eikonal model from cardiac Electro-Anatomical Maps is able to reconstruct the activation map from sparse recordings in the left atrium by fitting the local conduction properties of a patient-specific model. The first aim of this work was to employ PIEMAP in a cohort of patients who underwent electro-anatomic mapping right before pulmonary veins isolation (PVI). Secondly, we tested the ability of the method to predict the activation map in regions where no data were available. Data were selectively removed in the early, mid, and late activated regions. Finally, we studied the inter-patient variability of the estimated conduction parameters, namely, the fibre directions and the CV along and across the fibres.
Methods
Study population
The cohort of patients was collected consecutively at Fondazione Cardiocentro Ticino (Lugano, Switzerland) and retrospectively included in this study. All patients underwent a first single-PVI procedure for symptomatic paroxysmal or persistent AF. Patients being in AF at the time of the PVI procedure or who did not consent to study participation were excluded.
Oral and written informed consent for the PVI procedure was obtained from each patient. The study was approved by the internal review boards of each respective institution and by the local ethics committee.
Data acquisition
An electrophysiological study of the left atrium was performed before and after PVI using a 3-D electroanatomical mapping system (CARTO3 system with PENTARAY mapping catheter, Biosense Webster, Diamond Bar, CA, USA). A high-density EAM of the endocardial surface of the left atrium (LA) was acquired during sinus rhythm while simultaneously recording the 12-lead ECG. Bipolar electrograms and 3-D spatial position of the electrode were recorded with the mapping catheter at a temporal resolution of 1 kHz and 100 Hz, respectively. Recordings were aligned to the R-peak of the ECG. Recordings were automatically filtered to exclude those with (i) insufficient contact with the endocardium as indicated by the system; (ii) sliding electrodes using temporal position >1 cm, (iii) discrepancy of >20 ms between local activation time (LAT) from the system and the timing of the steepest negative deflection in the unipolar electrogram after a Savitzky-Golay filter of order 2 and frame length 21; (iv) inconsistent surface ECG; and (v) low unipolar amplitude (<0.07 mV).
The triangular mesh anatomy of the left atrium was automatically generated by the mapping system using the recorded positions of the electrodes. The mesh was resampled to a resolution of ∼1.7 mm to avoid problems with degenerated triangles. The measured points were projected onto the resampled mesh. The coverage of the EAM was obtained by taking the surface area within 10 mm from any measurement point divided by the total area.
Propagation model
Personalized Inverse Eikonal model from cardiac Electro-Anatomical Maps
The method to estimate the distributed conductivity tensor from EAMs of the left atrium was previously described (see also Figure 1).7 In summary, PIEMAP fits the tensor field such that the mismatch between the simulated activation map and the EAM at sampled locations is minimized in the least-squares sense. From a mathematical viewpoint, the EAM was a set of pairs with and being, respectively, the location and the activation time of the -th collected point. Personalized Inverse Eikonal model from cardiac Electro-Anatomical Maps solved the following problem:

Overview of the workflow to extract the fibres and conduction velocity from electro-anatomical mapping data using PIEMAP. The patient data, containing surface ECG, position, and the local activation time derived from the unipolar electrograms (UEG), are pre-processed to discard unreliable signals. The measurements are then used by PIEMAP to optimize a patient-specific model of the left atrium. The iterative process implemented into PIEMAP seeks for the optimal conductivity tensor (fibre directions and conduction velocities) that minimizes the mismatch between recorded and simulated activation times. PIEMAP, Personalized Inverse Eikonal model from cardiac Electro-Anatomical Maps.
The regularization term , based on a smooth approximation of the total variation, ensured the stability of the inverse reconstruction: Total-variation has shown to allow for variation of tissue conductivity in our previous study7 while also allowing sharp discontinuities in conduction velocities, as can be encountered in scarred tissue. The parameter was chosen by using a cross-validation technique: of the points were randomly removed from the fitting and eventually used to assess the quality of the reconstruction. We chose the associated with the lowest cross-validation error. The numerical solution was based on a primal-dual algorithm with a log-Euclidean formulation of , ensuring positive definiteness of the tensor field at all times, and implemented in TensorFlow on GPGPU with automatic computation of sensitivities.9,10
Estimate of fibre directions and conduction velocity
Fibre direction and CV along and orthogonal to the fibres were estimated from the Eigen decomposition of the conductivity tensor . The fibre direction was identified as the eigenvector corresponding to the largest eigenvalue. The eigenvalue provided the CV in the fibre direction. The second eigenvalue was associated with the CV across the fibres. The anisotropic ratio was defined as the ratio between the largest and the lowest eigenvalue. The front velocity was estimated by evaluating the conductivity tensor in the propagation direction.
Validation
Validation was performed by removing 20% of the measurements randomly and clustered in early activated regions and late activated region and then evaluating the error in prediction of the model. Simulations were also run to validate the ability of PIEMAP to extrapolate when measurements are not available. These validation sets contained 20% of the measurements in the form of a cluster in either an early, mid, or late activated region or in a random sparse set.
Data analysis
Fitted and recorded LAT maps were compared pointwise in terms of pairwise linear correlation coefficient. In the case of differing resolutions, correlation was performed on the lowest resolution. All other quantities are reported in mean±standard deviation.
Results
Nine patients fulfilling inclusion criteria were included in the analysis. In total, 9013 intracardiac contact recordings (1001 ± 499) were acquired in the electrophysiology studies, with an average of 2.5 simultaneous signals per beat (Table 1). Approximately 79% of measurement points (789 ± 425) were accepted by the pre-processing step and were used in PIEMAP. The coverage was as high as 70% with the exception of Patient #4 (35%) and Patient #7 (50%).
Patient . | # Beats . | # Rec. (rec./beat) . | Valid rec. . | Coverage (%) . |
---|---|---|---|---|
1 | 276 | 699 (2.5) | 517 (74%) | 71 |
2 | 458 | 1211 (2.6) | 993 (82%) | 73 |
3 | 392 | 856 (2.2) | 685 (80%) | 80 |
4 | 419 | 1104 (2.6) | 905 (82%) | 35 |
5 | 638 | 1657 (2.6) | 1309 (79%) | 77 |
6 | 199 | 414 (2.1) | 319 (77%) | 61 |
7 | 189 | 421 (2.2) | 261 (62%) | 50 |
8 | 265 | 822 (3.1) | 612 (75%) | 80 |
9 | 646 | 1829 (2.8) | 1500 (82%) | 82 |
Overall | 387 ± 173 | 1001 ± 499 | 789 ± 425 | 68 ± 16 |
Patient . | # Beats . | # Rec. (rec./beat) . | Valid rec. . | Coverage (%) . |
---|---|---|---|---|
1 | 276 | 699 (2.5) | 517 (74%) | 71 |
2 | 458 | 1211 (2.6) | 993 (82%) | 73 |
3 | 392 | 856 (2.2) | 685 (80%) | 80 |
4 | 419 | 1104 (2.6) | 905 (82%) | 35 |
5 | 638 | 1657 (2.6) | 1309 (79%) | 77 |
6 | 199 | 414 (2.1) | 319 (77%) | 61 |
7 | 189 | 421 (2.2) | 261 (62%) | 50 |
8 | 265 | 822 (3.1) | 612 (75%) | 80 |
9 | 646 | 1829 (2.8) | 1500 (82%) | 82 |
Overall | 387 ± 173 | 1001 ± 499 | 789 ± 425 | 68 ± 16 |
Patient . | # Beats . | # Rec. (rec./beat) . | Valid rec. . | Coverage (%) . |
---|---|---|---|---|
1 | 276 | 699 (2.5) | 517 (74%) | 71 |
2 | 458 | 1211 (2.6) | 993 (82%) | 73 |
3 | 392 | 856 (2.2) | 685 (80%) | 80 |
4 | 419 | 1104 (2.6) | 905 (82%) | 35 |
5 | 638 | 1657 (2.6) | 1309 (79%) | 77 |
6 | 199 | 414 (2.1) | 319 (77%) | 61 |
7 | 189 | 421 (2.2) | 261 (62%) | 50 |
8 | 265 | 822 (3.1) | 612 (75%) | 80 |
9 | 646 | 1829 (2.8) | 1500 (82%) | 82 |
Overall | 387 ± 173 | 1001 ± 499 | 789 ± 425 | 68 ± 16 |
Patient . | # Beats . | # Rec. (rec./beat) . | Valid rec. . | Coverage (%) . |
---|---|---|---|---|
1 | 276 | 699 (2.5) | 517 (74%) | 71 |
2 | 458 | 1211 (2.6) | 993 (82%) | 73 |
3 | 392 | 856 (2.2) | 685 (80%) | 80 |
4 | 419 | 1104 (2.6) | 905 (82%) | 35 |
5 | 638 | 1657 (2.6) | 1309 (79%) | 77 |
6 | 199 | 414 (2.1) | 319 (77%) | 61 |
7 | 189 | 421 (2.2) | 261 (62%) | 50 |
8 | 265 | 822 (3.1) | 612 (75%) | 80 |
9 | 646 | 1829 (2.8) | 1500 (82%) | 82 |
Overall | 387 ± 173 | 1001 ± 499 | 789 ± 425 | 68 ± 16 |
Reconstruction of activation map
The cross-validation analysis for the value of the regularization parameter showed that was optimal for all patients. The activation map as reproduced by PIEMAP showed an excellent correlation to recorded data (overall r = 0.96). Patients #4 and #6 showed a lower correlation (r = 0.62 and r = 0.74), whereas in seven patients (78%) correlation was between 0.93 and 0.97 (Table 2). Overall, activation maps reconstructed by PIEMAP were smoother than those reported by the mapping system. Bland–Altman analysis showed no bias with respect to measurements and limits-of-agreement were, respectively, –22.2 and 23.0 ms.
The first column shows the coverage, which is the percentage of surface that is within 1 cm distance from a measurement
Patient . | Reconstruction error . | Validation . | ||||||
---|---|---|---|---|---|---|---|---|
. | PIEMAP vs. measurements . | PIEMAP vs. interpolation . | Cluster . | Sparse . | ||||
. | Corr . | Error (mV) . | Corr . | Error (mV) . | Early . | Mid . | Late . | . |
1 | 0.93 | 5.30 | 0.86 | 8.83 | −0.46 | 0.50 | 0.56 | 0.87 |
2 | 0.96 | 5.52 | −0.21 | 528.28 | −0.25 | 0.69 | 0.58 | 0.95 |
3 | 0.97 | 4.58 | 0.89 | 10.03 | 0.84 | 0.92 | 0.80 | 0.96 |
4 | 0.62 | 22.84 | 0.09 | 91.68 | −0.07 | 0.30 | −0.29 | 0.57 |
5 | 0.93 | 6.68 | 0.92 | 10.98 | 0.75 | 0.69 | 0.61 | 0.91 |
6 | 0.74 | 11.84 | 0.80 | 20.05 | 0.57 | 0.44 | 0.49 | 0.66 |
7 | 0.96 | 5.69 | 0.51 | 23.43 | −0.41 | 0.13 | −0.09 | 0.88 |
8 | 0.97 | 3.29 | 0.86 | 9.82 | 0.89 | 0.91 | 0.69 | 0.96 |
9 | 0.97 | 4.28 | −0.32 | 1010.49 | 0.79 | 0.83 | 0.78 | 0.96 |
Overall | 0.96 | 7.8 ± 6.6 | −0.01 | 190 ± 350 | 0.77 | 0.86 | 0.88 | 0.95 |
Patient . | Reconstruction error . | Validation . | ||||||
---|---|---|---|---|---|---|---|---|
. | PIEMAP vs. measurements . | PIEMAP vs. interpolation . | Cluster . | Sparse . | ||||
. | Corr . | Error (mV) . | Corr . | Error (mV) . | Early . | Mid . | Late . | . |
1 | 0.93 | 5.30 | 0.86 | 8.83 | −0.46 | 0.50 | 0.56 | 0.87 |
2 | 0.96 | 5.52 | −0.21 | 528.28 | −0.25 | 0.69 | 0.58 | 0.95 |
3 | 0.97 | 4.58 | 0.89 | 10.03 | 0.84 | 0.92 | 0.80 | 0.96 |
4 | 0.62 | 22.84 | 0.09 | 91.68 | −0.07 | 0.30 | −0.29 | 0.57 |
5 | 0.93 | 6.68 | 0.92 | 10.98 | 0.75 | 0.69 | 0.61 | 0.91 |
6 | 0.74 | 11.84 | 0.80 | 20.05 | 0.57 | 0.44 | 0.49 | 0.66 |
7 | 0.96 | 5.69 | 0.51 | 23.43 | −0.41 | 0.13 | −0.09 | 0.88 |
8 | 0.97 | 3.29 | 0.86 | 9.82 | 0.89 | 0.91 | 0.69 | 0.96 |
9 | 0.97 | 4.28 | −0.32 | 1010.49 | 0.79 | 0.83 | 0.78 | 0.96 |
Overall | 0.96 | 7.8 ± 6.6 | −0.01 | 190 ± 350 | 0.77 | 0.86 | 0.88 | 0.95 |
Activation maps (PIEMAP, measurements, and CARTO) are compared on the left side using the correlation and the average absolute difference. Validation of the PIEMAP activation map is shown on the right side. The correlation of the validation set (20% of measurements) is depicted for clusters in early, mid, and late activated regions and for three times randomly selected sparse measurements. In the last row, either the overall correlation or the average±standard deviation is depicted.
PIEMAP, Personalized Inverse Eikonal model from cardiac Electro-Anatomical Maps.
The first column shows the coverage, which is the percentage of surface that is within 1 cm distance from a measurement
Patient . | Reconstruction error . | Validation . | ||||||
---|---|---|---|---|---|---|---|---|
. | PIEMAP vs. measurements . | PIEMAP vs. interpolation . | Cluster . | Sparse . | ||||
. | Corr . | Error (mV) . | Corr . | Error (mV) . | Early . | Mid . | Late . | . |
1 | 0.93 | 5.30 | 0.86 | 8.83 | −0.46 | 0.50 | 0.56 | 0.87 |
2 | 0.96 | 5.52 | −0.21 | 528.28 | −0.25 | 0.69 | 0.58 | 0.95 |
3 | 0.97 | 4.58 | 0.89 | 10.03 | 0.84 | 0.92 | 0.80 | 0.96 |
4 | 0.62 | 22.84 | 0.09 | 91.68 | −0.07 | 0.30 | −0.29 | 0.57 |
5 | 0.93 | 6.68 | 0.92 | 10.98 | 0.75 | 0.69 | 0.61 | 0.91 |
6 | 0.74 | 11.84 | 0.80 | 20.05 | 0.57 | 0.44 | 0.49 | 0.66 |
7 | 0.96 | 5.69 | 0.51 | 23.43 | −0.41 | 0.13 | −0.09 | 0.88 |
8 | 0.97 | 3.29 | 0.86 | 9.82 | 0.89 | 0.91 | 0.69 | 0.96 |
9 | 0.97 | 4.28 | −0.32 | 1010.49 | 0.79 | 0.83 | 0.78 | 0.96 |
Overall | 0.96 | 7.8 ± 6.6 | −0.01 | 190 ± 350 | 0.77 | 0.86 | 0.88 | 0.95 |
Patient . | Reconstruction error . | Validation . | ||||||
---|---|---|---|---|---|---|---|---|
. | PIEMAP vs. measurements . | PIEMAP vs. interpolation . | Cluster . | Sparse . | ||||
. | Corr . | Error (mV) . | Corr . | Error (mV) . | Early . | Mid . | Late . | . |
1 | 0.93 | 5.30 | 0.86 | 8.83 | −0.46 | 0.50 | 0.56 | 0.87 |
2 | 0.96 | 5.52 | −0.21 | 528.28 | −0.25 | 0.69 | 0.58 | 0.95 |
3 | 0.97 | 4.58 | 0.89 | 10.03 | 0.84 | 0.92 | 0.80 | 0.96 |
4 | 0.62 | 22.84 | 0.09 | 91.68 | −0.07 | 0.30 | −0.29 | 0.57 |
5 | 0.93 | 6.68 | 0.92 | 10.98 | 0.75 | 0.69 | 0.61 | 0.91 |
6 | 0.74 | 11.84 | 0.80 | 20.05 | 0.57 | 0.44 | 0.49 | 0.66 |
7 | 0.96 | 5.69 | 0.51 | 23.43 | −0.41 | 0.13 | −0.09 | 0.88 |
8 | 0.97 | 3.29 | 0.86 | 9.82 | 0.89 | 0.91 | 0.69 | 0.96 |
9 | 0.97 | 4.28 | −0.32 | 1010.49 | 0.79 | 0.83 | 0.78 | 0.96 |
Overall | 0.96 | 7.8 ± 6.6 | −0.01 | 190 ± 350 | 0.77 | 0.86 | 0.88 | 0.95 |
Activation maps (PIEMAP, measurements, and CARTO) are compared on the left side using the correlation and the average absolute difference. Validation of the PIEMAP activation map is shown on the right side. The correlation of the validation set (20% of measurements) is depicted for clusters in early, mid, and late activated regions and for three times randomly selected sparse measurements. In the last row, either the overall correlation or the average±standard deviation is depicted.
PIEMAP, Personalized Inverse Eikonal model from cardiac Electro-Anatomical Maps.
Three illustrative cases are reported in Figure 2. In Patient #3 (Figure 2A1 and A2) and Patient #5 (Figure 2B1 and B2), the activation map provided by the mapping system was clearly showing a single breakthrough in the Bachmann’s bundle region. The reconstruction accurately reproduced the recorded map (r = 0.89 and r = 0.92) and correlation to measurement points was excellent (r = 0.97 and r = 0.93). In Patient #7 (Figure 2C1 and C2), the recorded map showed multiple breakthrough sites in the right posterior pulmonary vein (PV) and in the LA roof, partially overshadowing the intrinsic activation from the Bachmann’ bundle. Initial PIEMAP reconstruction showed poor correlation (r close to zero). After removing ectopic points from the measurements, correlation significantly improved (r = 0.96).

Detailed reconstruction for Patients #3, #5, and #7 (from left to right). First row shows the LAT map from the EAM with in white the corresponding contours. In black, the contours of the PIEMAP LAT map are shown. Second row shows the PIEMAP LAT map with the corresponding contours in black. The measurements that were used by PIEMAP are depicted as a sphere in the colour of their LAT value. The third row shows the CV map with on top the contours of PIEMAP (black) and the fibre direction (black stripes). In the histograms, the distribution of the CV is shown. CV, conduction velocity; EAM, electro-anatomical map; LAT, local activation time; PIEMAP, Personalized Inverse Eikonal model from cardiac Electro-Anatomical Maps.
Reconstruction of conduction velocity
Conduction velocity was almost everywhere within 200 cm/s, with a limited number of exceeding values. In the fibre and in the cross-fibre directions, the velocity was, respectively, 82 ± 25 and 46 ± 7 cm/s. The estimated anisotropic ratio was 1.91±0.16. The front velocity was 77 ± 12 cm/s.
Conduction velocity in three exemplifying cases was within physiological expected boundaries with the exception of some high values in the region of the left PVs and interatrial bundles. The distribution of CV in each patient was almost symmetrical with mean between 50 and 100 cm/s. In Patient #7 (Figure 2C3), the distribution was narrower and on average lower than the average value across all the patients (P < 0.01).

Violin plot of the distribution of conduction velocity in the front direction (top) and in the fibre direction (bottom) for all patients.
Inter-patient variability
Figure 3 shows the distribution of the CV in all patients. Patients can be divided into two groups. In particular, one group included Patients #4, #6, and #7, which showed a significantly lower average CV (55 vs. 80 cm/s of the first group). Fibre velocity (Figure 3B) showed the same trend and was always higher than front velocity. Distribution and variability of CV was consistent across the patients, except in Patient #5, which showed a bimodal distribution in the fibre velocity.
Validation of the propagation model
Table 2 shows the correlation between PIEMAP prediction in activation for various validation sets. Overall variability in correlation was high (-0.41 to 0.96). In general, correlation was excellent in the case of random removal of data (r = 0.95), very good when points removed were in the late and mid-activated region (r = 0.88 and 0.86) and modest when points in the early activated region were removed (r = 0.77).
Discussion
In this study, we provided a proof-of-concept demonstration of PIEMAP, a first-of-its-kind framework for simultaneously estimating from a single EAM the regional CVs in the fibre and cross-fibre direction, the activation map and the fibre direction itself in the left atrium and not simply the front velocity. Personalized Inverse Eikonal model from cardiac Electro-Anatomical Maps is fully compliant with physiologically based models in the sense that the estimated CV can accurately reproduce the observed activation map. By its model-based nature and differently from purely data-driven approaches, PIEMAP can also forecast the activation in unmapped regions, hence potentially reducing total mapping time.
Accuracy
In general, PIEMAP was able to reproduce the activation map provided by the mapping system with high accuracy both in terms of correlation and absolute error. While point measurements were accurately reproduced, we noticed some discrepancies between the activation from PIEMAP and the interpolated activation from the mapping system. In three patients (#2, #4, and #9), the difference was particularly pronounced. In Patient #4, the low correlation was probably due to the low coverage of the EAM, hence making the extrapolation less robust. In Patients #2 and #9, however, deviations between PIEMAP reconstruction and the interpolated map were more pronounced in the PV region. This may be explained by the presence of ectopic activity, with several points around the PV activating very early with respect to the surrounding tissue—a common situation in patients with history of AF.11 These points were excluded by PIEMAP in the pre-processing step, yielding the observed difference between the methods.
The computed CVs showed a marked anisotropic conduction, as known in the literature, with anisotropic ratio in line with previously reported values.3 Moreover, the computed wavefront velocity was within the range (68–78 cm/s) of the CV derived from ultra-density mappings.12 The accuracy in reconstructing fibre direction is however difficult to establish. In a previous study,7 based on synthetic data, PIEMAP was able to correctly capture CVs, fibre directions and anisotropic ratio except around the PVs openings and the mitral valve ring. It is known that fibre architecture in the atria is particularly complex, with several endocardial bundles and fibres that may abruptly change direction.13 Prior knowledge on fibres, possibly obtained from previous histological studies, may be introduced in PIEMAP via regularization to improve the accuracy.14 Similarly, CV is linked to intra- and extra-cellular electric conductivity, surface-to-volume ratio, and ionic dynamic, hence it could find an activation-independent validation.3
Comparison to existing methods
Personalized Inverse Eikonal model from cardiac Electro-Anatomical Maps operates differently from existing interpolation-based (or local) approaches.5,6 In fact, PIEMAP optimally weights the contribution from data and the prediction of the model: if data are scarce or even missing in a region, the model tries to fill the gap. Personalized Inverse Eikonal model from cardiac Electro-Anatomical Maps is also robust to measurement errors or noise because of the underlying model that enforces a global coherence in the activation map. It is for this reason that PIEMAP previously showed to perform better than local methods.7 Although local CV methods are generally computationally cheaper, they heavily depend on the quality and the quantity of the measurements. High-density maps with vast coverage of the LA may not be easy to acquire in practice due to clinical time constraints.
Model-based approaches are not new either.15,16 However, those methods either assume isotropic conduction or anisotropic conduction with fixed fibre structure. Personalized Inverse Eikonal model from cardiac Electro-Anatomical Maps is instead capable of recovering fibre distribution as well. Recently, an interpolation-based method to determine fibre direction and CV along the fibre has been proposed, but it relies on multiple activation maps, often not available.17
Personalized Inverse Eikonal model from cardiac Electro-Anatomical Maps correctly forecasts activation in unmapped regions
A unique feature of PIEMAP is the ability to extrapolate the activation map in a consistent manner. The experiments showed excellent correlation of prediction to measurements when data were sparsely removed or when a region (20% of the dataset) was not included at all. This may indicate that PIEMAP can operate well also when data are scarce or incomplete, a common situation in practice. The correlation was however modest when early activated regions were removed, possibly due to the need for a correct breakthrough detection that may have been compromised by the exclusion of an early region. It is important to remark that the prediction in not done by extrapolating the activation map, but rather by extrapolating the conductivity field and then simulating the corresponding activation, with a clear advantage from a physiological viewpoint. The extrapolation of the CV depends on the regularization term and data availability.
Clinical implications
Personalized Inverse Eikonal model from cardiac Electro-Anatomical Maps only requires data acquired by the electro-anatomic mapping system. It operates automatically with minimal or no manual intervention. Since PIEMAP can effectively extrapolate activation in regions with poor or absent catheter coverage, it may significantly reduce total mapping time with sensible benefits for the patients. As suggested by other studies, conduction properties as estimated by PIEMAP could potentially unveil slow conducting regions associated with scar or fibrosis.2
Study limitations
The geometry employed by PIEMAP directly originates from mapping system, with minimal intervention. Compared to CMR or CT, contact mapping-derived anatomies are less accurate with potential implications on the CV estimation. However, our approach does not require co-registration which may equivalently introduce uncertainty in the data. Dielectric-based systems may further improve the accuracy without requiring cardiac imaging.18
Personalized Inverse Eikonal model from cardiac Electro-Anatomical Maps requires a good estimate of true activation breakthroughs, which is currently done automatically. Ectopic activity, multiple breakthroughs, or simply noise in earliest activation may be problematic to handle in PIEMAP. A more advanced breakthrough site detection is already under development.
The optimization problem is a non-convex, non-linear problem, with the final result possibly depending on the initial guess for the conductivity tensor. The lack of uniqueness is more likely to occur when the EAM is very sparse or when the coverage is poor.
Conclusions
We proposed and analysed a novel method, named PIEMAP, to reconstruction the activation in the left atrium from sparse and noisy contact recordings by estimating fibre distribution and conduction velocities in a patient-specific model. The method has been retrospectively applied to nine patients undergoing PVs isolation with promising results. Fibre arrangement and regional CV is a potential indicator of structural remodelling and could therefore guide ablation therapy in a personalized modelling workflow. Moreover, by relying only on data extracted from the mapping system, PIEMAP could be seamlessly integrated in existing mapping systems to forecast activation in unmapped regions. Studies with activation-independent assessment of CV and fibre distribution are needed to further validate our approach.
Funding
This work was financially supported by the Theo Rossi di Montelera Foundation, the Metis Foundation Sergio Mantegazza, the Fidinam Foundation, the Swiss Heart Foundation, the SNSF under project grant 32003B_165802, the Horten Foundation to the Center for Computational Medicine in Cardiology and the BioTechMed Graz grant ILearnHeart. Computer simulations were supported by the CSCS Swiss National Supercomputing Centre (production grant s778). This paper is part of a supplement supported by an unrestricted grant from the Theo-Rossi di Montelera (TRM) foundation.
Conflict of interest: A.A. is a consultant to Boston Scientific, Backbeat, Biosense Webster, Cairdac, Corvia, Microport CRM, EPD-Philips, and Radcliffe Publisher. He received speaker fees from Boston Scientific, Medtronic, and Microport. He participates in clinical trials sponsored by Boston Scientific, Medtronic, and EPD-Philips. He has intellectual properties with Boston Scientific, Biosense Webster, and Microport CRM. U.S. received consultancy fees or honoraria from Roche Diagnostics (Switzerland), EP Solutions Inc. (Switzerland), and Johnson & Johnson Medical Limited (United Kingdom). He is co-founder and shareholder of YourRhythmics BV, a spin-off company of the University Maastricht. All other co-authors do not have conflict of interest to disclose.
Data availability
The data underlying this article cannot be shared publicly for the privacy of individuals who participated in the study. The data will be shared on reasonable request to the corresponding author.