Fig 1.
Point Cloud Data (PCD) Model Generation.
The several steps to generate left atrial posterior wall (LAPW) PCD models are shown. First, the extracted LAPW points are downsampled. After downsampling, a surface mesh is created. This surface mesh is then extruded a specific thickness (2.3 mm in this work) to create a volume representing the LAPW. This volume is then meshed and refined to solve electrophysiology models in it. After mapping fiber orientations and determining stimulus sites, the model can be used along with other mathematical models such as the monodomain and Courtemanche models to simulate cardiac electrical propagation.
Fig 2.
The 3D geometry shows dimensions with fiber orientations for both patient H1A (left) and H1B (right). Blue points are electrode locations in space and red points in the geometry are points that were stimulated. These patient models did not have any atrial fibrosis added to their tissue substrates.
Table 1.
Waveform Characteristics Comparison. Summary of mean and standard deviation for all the characteristic parameters across all the signals is shown for both patient and simulated data for H1A and H1B. For both patients, the Cohen’s d value was calculated to measure the effect size of the recorded-simulated characteristics’ differences taking into account that there were 606 and 855 electrograms for patient H1A and H1B respectively. Typically, a Cohen’s d value smaller than 0.2 indicates an almost negligible effect size (unshaded in the table). Values between 0.2 and 0.5 indicate small but noticeable effect size (shaded light grey in the table), while values between 0.5 and 0.8 indicate moderate or medium effect size (shaded medium grey in the table). Cohen’s d values greater than 0.8 typically indicate very large effect size representing a significant disparity in this case between recorded and simulated electrogram characteristics (shaded dark grey in the table).
Table 2.
Error and Correlation Values. Error mean and standard deviation values for peak-peak amplitude, deflection count, EGM duration, and LAT across all the signals from both H1A and H1B are shown along with correlation coefficients of electrograms and cross-correlation peak averages for their normalized versions. LATs error were the smallest of all of them meaning that activation of the simulations happened around the same time as the measured EGMs indicated. The largest error was peak-peak amplitude for both patients which probably affected correlation coefficients being low. The average cross-correlation peaks increased substantially after amplitude normalization, highlighting the influence of amplitude on the signal comparison.
Fig 3.
Patients H1A and H1B Principal Component Space.
Measured and simulated signals’ PCs coming from patient H1A (left) and H1B (right) are shown using detail coefficients coming from a fourth-order wavelet decomposition on all the measured waveforms of the patients. These PCs coming from measured EGMs were clustered into three different clusters while their eigenvectors were used to map the simulated signals in the same PC space (cyan color). The axes show the first three PCs while the size of each data point corresponds to the fourth PC. Via clustering and visualization, simulated signals fell within the measured signals PCA space. Some of these points lied very closely to other measured signal points, meaning that they simulated some of the signals within the clusters well. Other points lie farther from the clinically measured signals cluster, meaning that those points probably differed more in morphology compared to the measured signals. The models’ performance in simulating EGMs using the detail coefficients metric could be visualized graphically using PCA.
Fig 4.
Patients H1A and H1B Sample Clustered Signals.
Sample signals (both measured and corresponding simulated) are shown from the different PCA clusters for patients H1A (left) and H1B (right). Even though for PCA generation the normalized signals were used due to the focus on morphology, the signals shown are in mV. The x-axis represents time in msec, and the y-axis represents the extracellular potential in mV, with the left axis corresponding to the measured signal and the right axis to the simulated signal. Two different axes were used to aid in the morphology comparison, since different amplitudes can hinder visual interpretation. The colors correspond to the PCA clusters shown in Fig 3. As observed, some components of the signals were very similar (e.g., the blue signals probably had the same downstroke time). The blue signals even exhibit nicely rounded deflections. Some other components, such as the amplitudes, were not as well captured. The activation times of the pink lines, for instance, differed greatly from one another.
Table 3.
PCA-based Model Performance. Information about the PCA space distance-to-centroid for the recorded and simulated EGMs PCs is shown. The average PC distance from each recorded EGM PCs to its cluster centroid was calculated, as well as the distance-to-centroid for each simulated EGMs PCs to its corresponding measured waveform counterpart cluster centroid (“common”) and the actual closest cluster centroid of the simulated waveform (“closest”). Because of the disparity between common and closest cluster centroids, the percentage at the end shows the fraction of EGMs whose simulated counterpart belonged to a different cluster; as seen, more than 50% of the simulated EGMs belonged to a different cluster than their recorded counterparts. Simulated EGMs distance-to-centroid values were significantly larger than their measured counterparts even in the closest cluster cases.
Fig 5.
Patients H1A and H1B Isosurfaces.
Isosurface maps on all surface points are shown for patients H1A (left) and H1B (right) usin LAT mapping based on electrode proximity for recorded (top) and simulated (bottom) signals. Colorbars show the limits for each surface. The axes are x, y, and z in space. The simulated signal isosurfaces have smoother transitions between LAT ranges compared to the recorded signals. In contrast, the recorded signal isosurfaces had many patches of differing LATs. Even though many points and regions coincided between simulated and recorded data, the recorded EGMs isosurfaces suggest abnormal propagation patterns, as activation occurs in an irregular manner.
Fig 6.
Sample of random signal pairs are shown for points of interest seen in Fig 2 for patient H1A. Blue and orange lines represent recorded and simulated signals, respectively. The x axis represents time in msec, and the y-axis represents electric potential in mV. As seen in the plots, some characteristics of the measured signals were mostly correctly simulated with the models (i.e., timing) while others were not fully captured like amplitudes.
Fig 7.
Sample of random signal pairs are shown for points of interest seen in Fig 2 for patient H1B. Blue and orange lines represent recorded and simulated signals, respectively. The x axis represents time in msec, and the y-axis represents electric potential in mV. As seen in the plots, the waveform morphologies in patient H1B seem to be more similar compared to patient H1A. The timings were different, but the characteristics looked better. This comparison can be seen in Tables 1 and 2 as well.
Table 4.
Simulated EGMs Characteristics Variability (Atrial Fibrosis Degree and Type). The table shows the characteristic parameters variability across the combinations of different types and degrees of fibrosis. For each combination, the parameters are given in average and standard deviation values. From the table, it can be seen that the differences between the characteristics are more sensitive to fibrosis degree compared to fibrosis density. For instance, the mean and standard deviations of EGM durations and deflection counts seem to have increased as the fibrosis density increased, but the mean and standard deviation of the peak-peak amplitude values seem to decrease with increasing fibrosis density. On the other hand, there is no significant distinction in characteristic parameters values between types of fibrosis for all the fibrosis densities. These observations were confirmed with the statistical test done and shown in Table 5.
Table 5.
One-way ANOVA and Tukey’s Significant Differences. The table shows the results of the statistical test performed on the differences between EGM duration, Peak-to-peak amplitude, and deflection count metrics across the different fibrosis simulation groups. The results demonstrated that fibrosis percentage (10%, 35%, 60%) had a consistently strong effect on electrogram features across all fibrosis morphologies (F = 5,562–68,087, p < 0.0001), with Tukey’s post-hoc confirming that every pair of percentages was significantly different. In contrast, while fibrosis type (diffuse, compact, patchy, interstitial) also produced significant differences at fixed percentages (F = 16.7–3,064, p < 0.0001), certain morphologies (e.g., diffuse vs interstitial at 10% and 35%) did not differ significantly. Even though the different fibrosis types produced significant differences, the much higher F-statistic values for differences in fibrosis degree compared to fibrosis type indicate that fibrosis percentage is the dominant determinant of electrogram alterations, with morphology exerting secondary, less consistent effects.
Fig 8.
Fibrotic Models Samples with Sample Random Signal Pairs.
Fibrotic tissue and recorded-simulated electrogram signals pair for sample fibrotic patterns for the four different model geometries used in fibrotic simulations. Different fibrotic patterns for four different patient-specific models (H2B, H2C, H2D, and H2E) are shown with the resulting local activation times map (color-coded according to colorbar). Sample signal pairs of recorded and simulated electrograms are also shown to display model performance in simulating some of the electrogram waveforms recorded in the clinic. As seen, some components are nicely captured (i.e., general morphology, some activation times) while other components were not fully obtained (i.e., amplitude). These waveforms were characterized for all simulations to obtain Table 4.
Fig 9.
A) Additional randomly selected electrode points based on locations are shown: towards the beginning of propagation (top left), towards the middle of the tissue domain (top right), close to tissue curvature (bottom left), and towards the end of propagation (bottom right). Blue and orange lines represent the recorded and simulated traces, respectively. The x and y axes are time (msec) and amplitude (mV), respectively. Amplitude and morphology similarities are shown, while also the presence of more deflections in healthy tissue configuration than a biphasic signal is shown. B) Sample signals for patient H1B are shown selected based on location: from an electrode point right before the side edge of the geometry (top) and an electrode point past the edge of the geometry (bottom). Blue and orange lines represent the recorded and simulated traces, respectively; the x and y axes are time (msec) and amplitude (mV), respectively. Far-field activity happening in the recorded signals was not seen in the simulated signals as shown.
Fig 10.
Sample Waveforms from Fibrosis Simulations.
Selected sample waveforms with morphologies comparable to the computational study done by Campos et al. Campos and colleagues simulated patterns with uncoupled tissue with orientations parallel to muscle fibers (similar to interstitial or patchy fibrosis) and orientations with multiple random directions (similar to diffuse fibrosis). Since in their work they had these densities as mid-level and higher-level fibrosis densities, sample waveforms are shown for fibrosis simulations with set-ups more closely similar to the ones from Campos’ work. Electrograms with similar morphologies are shown for these two types of tissues; these electrograms come from one of the simulation configurations with 35% interstitial fibrosis and another simulation configuration with a 60% diffuse fibrosis. As seen, morphological characteristics like deflection patterns and amplitudes are comparable to the results from Campos et al., speaking to the ability of PCD models to generate waveforms comparable to published studies.