Intracardiac Inverse Potential Mapping Using the Method of Fundamental Solutions

FIGURE 1. Schematic representation of the intracardiac forward problem. Fictitious electrical sources (open circles) distributed around a virtual boundary ΓV outside the surface ΓH that bounds a heart cavity ΩH generate current flux within the domain. This contributes to potentials recorded with electrodes (closed circles) on a basket catheter. The electrodes lie on the open surface ΓC .

FIGURE 2. In silico analysis of the effects of mapping catheter dimension and electrode distribution on MFS inverse solutions during pacing from distal coronary sinus. Ground-truth LA surface potential distributions during atrial activation are constructed from pace-synchronized contact recordings acquired with a high density electrode array. Corresponding potential fields in the LA cavity are estimated throughout the atrial activation cycle and “sampled” at locations of virtual basket catheter electrodes. Inverse surface potential maps are then reconstructed from these data and compared with ground truth maps. (A) Ground-truth LA surface potential distribution at one instant during activation - see red line in (C). Corresponding inverse potential map (B) reconstructed from potentials sampled with virtual 64-electrode basket catheter with 0.67 volume fraction relative to LA. Electrodes are distributed uniformly along 8 splines as indicated in (A). (C) Ground truth and reconstructed electrograms at 1 in (A,B). In the middle panel, CC (D), nRMSE (E) and ΔT (F) are presented as functions of relative catheter volume for inverse solutions over one activation cycle. Median values and IQR are…

FIGURE 3. Effects of mapping catheter electrode distribution on inverse solutions with MFS during macro reentry. LA surface potentials throughout 3 activation cycles in simulated atrial flutter are reconstructed from electrograms sampled inside the LA cavity with 64- and 130-electrode basket catheters and compared with ground-truth surface potentials. The upper panel presents typical results for catheters that bound a volume fraction of 0.67 relative to LA volume. These include (A) the ground-truth surface potential distribution at one instant during reentrant activation and corresponding potential maps reconstructed using electrograms sampled with (B) a 64- electrode basket catheter, and (C) a 130-electrode basket catheter. In the lower panel CC (D), nRMSE (E) and ΔT (F) are presented as functions of relative catheter volume for the 64-electrode catheter (blue) and 130-electrode catheter (red). Median values and IQR are given. Abbreviations: MFS, Method of Fundamental Solutions; LA, left atrium; CC, correlation coefficient; nRMSE, normalized root-mean-squared error; ΔT, activation time difference; IQR, interquartile range.

FIGURE 4. Effects of noise on inverse solutions with the MFS during macro reentry. LA surface potentials throughout activation cycle in simulated atrial flutter are reconstructed from electrograms sampled inside the LA cavity using 130-electrode basket catheters with added Gaussian noise at different mean power levels. All data are compared with ground-truth endocardial potentials. In the upper panel (A) electrograms reconstructed from records acquired from a very small and a large basket catheter with 18, 56 and 178 μV of added noise are presented with the corresponding ground-truth electrogram. Catheter volumes relative to LA volume are 0.014 and 0.91, respectively. In the lower panel, CC (B), nRMSE (C) and ΔT (D) are presented as functions of relative catheter volume for the three noise levels. Median values and IQR are given. Abbreviations: LA, left atrium; CC, correlation coefficient; nRMSE, normalized root-mean-squared error; ΔT, activation time difference.

FIGURE 5. Phase maps of inverse solutions with MFS during macro-reentry. LA surface potentials throughout activation cycle in simulated atrial flutter are reconstructed from electrograms sampled inside the LA cavity using 64- and 130-electrode basket catheters. The centrally located catheters occupy 67% of LA volume. (A) Ground truth phase map at one instant during activation compared with corresponding phase maps for surface potentials reconstructed from electrograms recorded with 64-electrode and 130-electrode basket catheters. (B) CC and nRMSE presented as functions of relative catheter volume for the 64-electrode catheter (blue) and 130-electrode catheter (red). Median values and IQR are given. Abbreviations: MFS, Method of Fundamental Solutions; LA, left atrium; CC, correlation coefficient; nRMSE, normalized root-mean-squared error; IQR, interquartile range.

FIGURE 6. Comparison of region-of-interest inverse potential mapping with global mapping. LA surface potentials during 3 activation cycles of simulated macroscopic reentry were reconstructed from electrograms sampled inside the LA cavity with a small 64-electrode basket catheter. The catheter was initially positioned with some electrodes touching the wall at the junction with the LAA and then moved rightward until electrodes made contact with the inter-atrial septum. (A) Representative ground truth potentials on cavity surface also showing broken white line along which catheter is moved from origin of LAA (relative catheter position 0) to inter-atrial septum (relative catheter position 1). (B) Inverse solution reconstructed from potentials sampled at relative catheter position 0. (C) Correlation coefficient map for ground-truth and inverse solutions in this case. The RoI indicated is the smoothed boundary of the surface in (C) where CC ≥ 0.9. In the lower panel (D–F) present CC, nRMSE and ΔT, respectively, in the RoI (red) and across the complete LA surface (blue) for inverse solutions with the catheter at equi-spaced locations along the line in (A); catheter locations 0 and 1 are…