## 4 Discussion
### Benchmark Analysis of Meshless and Finite-Element Method Solutions on Training Data  
Despite the complex pipeline to process EAM data and the variability of the analyzed cases, the SPH-based model provided low LAT errors in LBBB (6.75 \(\pm\) 1.59 ms) and CRT (10.38 \(\pm\) 3.80 ms) cases. The meshless simulation results were generally similar to FEM-based ones from CRT-EPiggy19 participants (see Table 1 and Figure 5), when qualitatively analyzing the electrical activation patterns, and with the quantitative metrics (e.g., TAT, LAT, delays). However, some methodological differences were found that could explain small variations in the obtained results. For instance, the approach by [PERSON] and [PERSON] [29], using a biophysical Ten Tusscher-Panfilov model, with a larger number of parameters and a more personalized Purkinje system differentiating between RV and LV, will certainly be more appropriate than simplified phenomenological Eikonal models in some cases. On the other hand, the low computational cost of Eikonal-based solutions allow running a lot of simulations and a larger exploration of the parameter space to match EAM data. Computational times for both meshless and FEM-based methods depend on the domain resolution (i.e., number of points/elements), the complexity of the electrophysiological model, and the number of parameters to estimate in the optimization procedure. Moreover, there is also a variety of IT resources involved. Independently of these factors, the main advantage of the meshless methods is the time saved to prepare the simulation domain compared to FEM alternative, which can be a matter of hours for complex geometries. The key parameters related to the electrophysiological modeling for better fitting the EAM data were (1) the initial stimuli (number and position) of the electrical activation, (2) the modeling of the PK system, (3) and the regional conduction velocity distribution, which was optimized for each analyzed case. For instance, most participants [27; 29] and ourselves adapted their modeling solutions to consider a possible retrograde activation of the PK system, via an extra-stimulus, to replicate the rapid activation from the apex to the LV base observed in the EAM data. Figure 10 in the Appendix shows how using only one stimulus provided simulation results farther from the EAM data (error of 15.3 ms vs. 5.1 ms for two stimuli), demonstrating the dependence of the simulated activation patterns on the stimulation protocol. Potential causes for the PK retrograde activation might be the more transmural PK system in pigs compared to humans, which lead to incomplete LBBB such as in Pig 3 (anterior PK branch being functional while posterior branch being damaged, affecting the epicardial propagation). Modeling solutions with dedicated PK models such as in [29, 39] could explain their better performance in these cases, justifying the use of more detailed and personalized PK system estimation algorithms [46, 48]. The most important parameter to optimize in all electrophysiological modeling solutions to match EAM data were the regional distribution of conduction velocities, with computational costs directly linked to the chosen number of regions. We performed a sensitivity analysis that resulted in the use of 5 regions (RV/LV endocardium/ epicardium, PK system), which avoided overfitting of LBBB-estimated results when applied to CRT cases (effect seen with a larger number of regions) and reasonable computational times (e.g., around 20 min per simulation). The CV distribution provided by the SPH-based model (see Table 2) are physiologically meaningful (e.g., PK being the fastest region, endocardial regions faster than epicardial ones, the scar having the lowest CV values), due to the imposed constraints in the optimization step. [PERSON] and [PERSON] [28] used the same regions without PK in the only case they processed (Pig 3), however obtaining similar qualitative results in CRT simulations to [PERSON] and [PERSON] [29] and ourselves. The regional strategies selected by [PERSON] et al.