## 4 Discussion and Conclusions  
The present work demonstrates that the intra-recording and intra-patient stability assessment of CFAEs is significantly benefited by the exclusion of artifacted or noisy segments, thus helping to quantify the atrial electrophysiological substrate with reliable and representative values. By contrast, previous studies may lead to an oversimplification of the processes taking place at different regions of the atria, thus providing biased and unreliable results in the characterization of the atrial substrate. To this respect, the stability of the CFAE and their corresponding nonlinear indices are significantly influenced by the length of the analyzed segment, and specifically by the recording site within the left atrium (see Figure 3). In this regard, the number of discards in the LSPV have been quite low compared to the other recording places. In contrast, the RSPV has been the recording site in which the discards have been more frequent. This fact could be due to the difficulties in reaching the RSPV using a LassoTM catheter (Biosense-Webster, Diamond Bar, CA, USA), such as in the present study, in comparison with basket catheterization. In fact, catheters such as the ConstellationTM (Boston Scientific, Natick, MA, USA) have the advantage to better fit in most veins, adapting to size and anatomical form [48], their main disadvantage being the higher cost [49; 50]. The introduction of discards provoked the reduction in ranges and standard deviations both in the SE and DET (Tables 1 and 2), thus showing that mapping CFAE with contact catheters on a beating heart is a delicate task [48]. Furthermore, the discarding process benefited more the intra-recording stability (Table 3) than the intra-patient stability (Table 4), so that the CV varied more significantly in the first case. Nonetheless, the continued high variability of the CV suggests that averaging data in the same recording (intra-recording), as well as among recording places (intra-patient), may lead to an unfair oversimplification of the CFAE-based atrial electrophysiological substrate characterization, which has not been considered in many previous studies. In particular, in the intra-patient analyses, the visualized box plots exhibited many instances in which just a part of the recording places presented similar atrial electrophysiological properties as identified by like DET and SE values, enhancing the conclusion that averaging causes a loss of singularity of the electrophysiological substrate at the different atrial sites, which is the basis for the development of personalized catheter ablation procedures for AF treatment. Unlike other complicated previously published models, this work has also proved that it is possible to develop straightforward solutions for clinical practice able to discriminate between ParAF and PerAF from the CFAEs of patients undergoing catheter ablation, thus providing a more understandable insight for atrial substrate evaluation and improved therapeutic decisions for AF management. To this respect, the SE mean values diminished with the segment length (Table 5), with greater values in PerAF as compared to ParAF, thus reflecting a higher degree of disorganization in PerAF, which is in agreement with a previous study [22]. Similarly, the DET values increased with the segment length, showing greater values in ParAF versus PerAF, thus highlighting ParAF as more predictable than PerAF. The computation of the AFCL from the 16 s length CFAEs resulted in higher values for ParAF than for PerAR, as well as in lower values of DF for ParAF than for PerAF,as has been reported in prior work [40]. However, the discussion remains open in this respect, because other studies have reported DF peak frequencies higher in ParAF than in PerAF [51]. The study of the correlation between the indices and recording sites is illustrative (see Figure 4) because it showed a high correlation between the SE and DET in the same recording site.