Novel Computational Analysis of Left Atrial Anatomy Improves Prediction of Atrial Fibrillation Recurrence after Ablation

The left atrium (LA) can change in size and shape due to atrial fibrillation (AF)-induced remodeling. These alterations can be linked to poorer outcomes of AF ablation. In this study, we propose a novel comprehensive computational analysis of LA anatomy to identify what features of LA shape can optimally predict post-ablation AF recurrence. To this end, we construct smooth 3D geometrical models from the segmentation of the LA blood pool captured in pre-procedural MR images. We first apply this methodology to characterize the LA anatomy of 144 AF patients and build a statistical shape model that includes the most salient variations in shape across this cohort. We then perform a discriminant analysis to optimally distinguish between recurrent and non-recurrent patients. From this analysis, we propose a new shape metric called vertical asymmetry, which measures the imbalance of size along the anterior to posterior direction between the superior and inferior left atrial hemispheres. Vertical asymmetry was found, in combination with LA sphericity, to be the best predictor of post-ablation recurrence at both 12 and 24 months (area under the ROC curve: 0.71 and 0.68, respectively) outperforming other shape markers and any of their combinations. We also found that model-derived shape metrics, such as the anterior-posterior radius, were better predictors than equivalent metrics taken directly from MRI or echocardiography, suggesting that the proposed approach leads to a reduction of the impact of data artifacts and noise. This novel methodology contributes to an improved characterization of LA organ remodeling and the reported findings have the potential to improve patient selection and risk stratification for catheter ablations in AF.

In our problem the degrees of freedom of the computational mesh are heavily correlated, and this annex investigates the impact of different choices of the LDA regularization. The use of an intermediate shape space, the PCA space, as detailed in the main manuscript, is one possible solution.
Methods: An LDA of the mesh degrees of freedom is perform, without a preliminary PCA. Three possibilities are evaluated: (1) LDA without any regularization, (2) the inversion of the covariance matrix using the pseudo-inverse, (3) the use of the diagonal of the covariance matrix.

Results and Discussion:
Depending on the choice of regularization we have been able to identify qualitatively two possible solutions that split the population of 144 meshes, illustrated in Supplementary Figure 1: -Methods (1) or (2) (overfitted result): the LDA achieves a perfect, or almost perfect split of the population in resubstitution (AUC ~ 1), but a very poor performance in cross-validation (AUC ~ 0.5). The illustration of the extreme shapes encoded by the LDA mode displays very small changes in the anatomy (see top row in Figure A.1). This is an example of the "high dimension low sample" problem discussed in the main manuscript.
-Method (3) (reasonable result): using the diagonal of the covariance matrix the LDA obtains a positive classification outcome in cross-validation (leave-1 out, 0.62 and 0.58 at 12 and 24 months respectively), but below the performance of the PCA+LDA (0.65 and 0.65 of the oLDA, see main manuscript). Qualitatively the extreme shapes of the LDA mode at both time points, 12 and 24 months, are quite similar between them, but do not clearly show the changes in AP distance, sphericity or vertical asymmetry observed when using the PCA+LDA approach. We interpret that the loss of discriminative power and detail is driven by the loss of information through the process of only retaining the elements of the diagonal of the covariance matrix.

Conclusion:
The LDA regularization choice has an impact on results. The PCA + LDA strategy provides the best performance in terms of predictive power and interpretation of the remodeling pattern.

Choice of PCA Modes
In this part, we investigate how the predictive power of LDA depends on the truncation of the PCA performed prior to the LDA.
Methods: An exhaustive search of the optimal performance of the LDA over the PCA modes with different choices of the PCA modes to include was performed. The choice of PCA modes to include varied between choosing the 3 first modes to all first 15. Performance is evaluated by a leave-1 out AUC at both 12 and 24 months.

Results and Discussion:
No choice of PCA modes improved the cross-validation AUC compared to the choice of modes 1, 2 and 8 reported in the main manuscript. This result suggests that there is no further useful information for the purposes of recurrence prediction contained in the smaller modes beyond mode 8.
For illustrative purposes, we show the outcome of the LDA performed on the combination of modes 1, 2 and 5. This reveals a remodeling pattern where the extreme recurrent shape has very large: volume, AP distance, and sphericity, as reported in the literature (see Figure A.2 panel A).
The remodeling pattern captured with this choice of PCA modes (1, 2, 5) shows a larger deviation in shape relative to the mean than the oLDA (optimal combination of modes 1, 2 and 8) reported in the manuscript. This is because PCA mode 8 encodes a lower shape variance than mode 5. As modes with smaller variance gain a higher weight in the LDA, the extreme shapes computed deviate less from the mean shape.

Conclusion:
The choice of PCA modes 1, 2 and 8 provided the best discriminative performance and allowed for the observation of remodeling patterns beyond those explained by volume, AP distance and sphericity, namely by the metric we dubbed vertical asymmetry.

A) B)
Supplementary Figure 2. LDA analysis including modes 1, 2 and 5 (panel A) and modes 1, 2 and 8 (panel B) at 12 months. Each panel shows the linear coefficients found for each mode and the extreme shapes synthetized at +/-3 std, with the blue semi-transparent mesh corresponding to the extreme recurrent, and the yellow opaque to the extreme non-recurrent.