## 2 Materials and Methods
### Meshless Model Based on Smoothed Particle Hydrodynamics  
The total Lagrangian meshless method (TL-SPH) developed by [PERSON] et al. (2018) was used in our experiments. As a meshless model, SPH is easy to parallelize, and memory efficient. Additionally, it is mathematically rigorous since it satisfies the Kronecker's delta property. Figure 1 illustrates the developed meshless SPH-based modeling pipeline to predict CRT electrical patterns in the experimental data. The first step of the pipeline consisted on discretizing the continuous domain provided by the biventricular meshes of the porcine hearts with a cloud of particles without connectivity, where each particle had the following individual properties: three-dimensional position, cardiomyocyte orientation, tissue type, initial impulse, conduction velocity, area and volume.  
To determine the particle properties a Gaussian Kernel function was enforced, defining the number of neighboring particles around each particle of interest that is then employed  
Figure 1: Scheme of the developed meshless modeling pipeline to predict the electrical patterns in experimental data after cardiac resynchronization therapy. LBBB: left bundle branch block. RMSE: root mean square error. LAT: local activation time.  
to estimate the area and volume indices. Parameters such as the kernel size (i.e., smoothness length of the Gaussian kernel) and the geometry discretization according to the number of particles were key factors to determine when setting up the simulation. To define the optimal values of the Gaussian kernel function, sensitivity analyses of particle resolution and kernel size were performed. Several simulations were carried out fixing the kernel size and increasing the particle numbers; configurations with 15 \(\times 10^{3}\) (2 h simulation), 20 \(\times 10^{3}\), 80 \(\times 10^{3}\) and 100 \(\times 10^{3}\) (11 h simulation) particles were studied in one of the analyzed geometries. The kernel size was inversely proportional to the number of particles to avoid excessive computational cost; kernels from 3.5 to 9 mm were tested in intervals of 0.5 mm. A kernel size of 6.5-8.5 mm was finally defined, as a function of the swine model morphology and required conduction velocities (i.e., larger kernels for higher conduction velocities and morphologies with higher curvature), in combination with geometries of 15 \(\times 10^{3}\) particles. As shown in [42], configurations with higher number of particles (e.g., 50 \(\times 10^{3}\)) and smaller kernel sizes (e.g., 3 mm), computational costs exponentially increases without a substantial accuracy gain, which will hamper the parameter optimization process. Furthermore, we also analyzed the effect of the time-step, testing values of \(10^{-3}\), \(10^{-4}\), and \(10^{-5}\) in one of the studied cases for LBBB simulations. The computational cost associated with each time-step value was of \(>\)42 min, around 20 min and around 7 min, providing RMSE of 6.2 ms, 6.8 ms, and 7.9 ms, respectively. A time-step value of \(10^{-4}\) was finally chosen as a trade-off between computational cost and result accuracy. The total simulated time was of 0.15 s, based on the total activation times of the available EAM dataset (i.e., most cases with TAT \(<\) 0.1 s).