Characterization of Electrophysiological Propagation by Multichannel Sensors

Abstract

Objective: The propagation of electrophysiological activity measured by multichannel devices could have significant clinical implications. Gastric slow waves normally propagate along longitudinal paths that are evident in recordings of serosal potentials and transcutaneous magnetic fields. We employed a realistic model of gastric slow wave activity to simulate the transabdominal magnetogastrogram (MGG) recorded in a multichannel biomagnetometer and to determine characteristics of electrophysiological propagation from MGG measurements.

Methods: Using MGG simulations of slow wave sources in a realistic abdomen (both superficial and deep sources) and in a horizontally-layered volume conductor, we compared two analytic methods (second-order blind identification, SOBI and surface current density, SCD) that allow quantitative characterization of slow wave propagation. We also evaluated the performance of the methods with simulated experimental noise. The methods were also validated in an experimental animal model.

Results: Mean square errors in position estimates were within 2 cm of the correct position, and average propagation velocities within 2 mm/s of the actual velocities. SOBI propagation analysis outperformed the SCD method for dipoles in the superficial and horizontal layer models with and without additive noise. The SCD method gave better estimates for deep sources, but did not handle additive noise as well as SOBI.

Conclusion: SOBI-MGG and SCD-MGG were used to quantify slow wave propagation in a realistic abdomen model of gastric electrical activity.

Significance: These methods could be generalized to any propagating electrophysiological activity detected by multichannel sensor arrays.

Figure 1

Boundary element skin and stomach models and sensors. (a) The stomach model, (b) the torso model with the 110 sensors in the hypothetical magnetometer system used to evaluate magnetic field propagation, and (c) the coronal place of sources and sensors in the torso model. The distances of SD and DD from the SQUID are 50 mm and 170 mm, respectively.

Figure 2

Magnetic field maps from (a) the SD, (b) DD, and (c) the HL source configurations used to characterize propagation velocity plotted every four seconds as a source dipole moves across the stomach from left-to-right. The map at the top corresponds to t = 4 s and the bottom map corresponds to the end of the sequence at t = 20 s. Magnetic fields at successive 4 s intervals are shown as the dipole traverses the gastric musculature. The location of the source dipole is shown as a circle in the field maps. The corresponding electric potential computed on the body surface from the SD configuration is also shown for comparison in (d). For (a)-(d), c_min/c_max = [±15pT, ±2 pT, ±15 pT, ±25 mV] , respectively.

Figure 3

SOBI reconstructions of the data in Figure 2 for the (a) SD, (b) DD and (c) HL source configurations. The location of the original source dipole is represented by a circle and the SOBI estimate of the dipole location by a cross. For (a)-(c), c_min/c_max, = [±5 pT, ±0.2 pT, ±2 pT], respectively.

Figure 4

Surface current density maps computed from magnetic fields in Figure 2 for (a) SD (b) DD and (c) HL source configurations. The location of the original dipole is represented by a circle and the SCD estimate of the dipole location by a cross. SD conformations corresponding to the double-lobed magnetic field patterns from a single dipole tend to show one predominant lobe whose maximum is centered above the dipole location. For (a)-(c), c_min = 0 A/m²; c_max are, respectively: [5.5, 0.2, 2.5] μA/m²

Figure 5

Dipole location estimates from SCD propagation method (squares) and the SOBI propagation method (circles ) in (a.i) superficial dipole, (b.i) deep dipole, and (c.i) horizontal layer models without noise. Actual dipole locations are represented by the solid line. The origin and termination of the propagating dipole sequences are indicated by the time in seconds; numbers are oriented normally for the actual dipole positions, leaning right for SOBI estimates and left for SCD. The performance of the algorithms in the presence of noise is illustrated by panels a.ii, b.ii, and c.ii for the SD, DD and HL models, respectively.

Figure 6

(a) Mean square error (MSE) between SCD and SOBI dipole location estimates and actual dipole location. (b) Correlation of SCD/SOBI dipole location estimate with actual dipole location. Squares mark SCD dipoles while circles represent SOBI estimates, with x positions represented by open symbols and y positions represented by filled symbols. Generally, SOBI estimates result in higher correlation with actual dipole positions and lower mean square error. (c) Accuracy of propagation velocity (PV) computation using the four methods in each of the different source configurations tested. Circles indicate propagation velocity estimated using SOBI and crosses indicate that the SCD method was used. The dotted line represents the actual propagation velocity. Generally, SOBI and SCD show comparable performance for computing propagation velocity in noise-free data with methods PV_B and PV_C showing the highest accuracy. SOBI propagation calculations tend to outperform SCD with noise except in the deep dipole configurations for methods PV_A and PV_B, PV_C.

Figure 7

Data from porcine experiment. (a) SCD map, (b) SOBI map, and (c) electrode platform recordings. The cross in (a) and (b) show the SCD and SOBI estimate of the underlying source. All show evidence of propagation of electrical activity. For (a) c_min/c_max = [0, 2.5] μA/m², and for (b) c_min/c_max = ±0.25 pT.

Figure 8

Results of propagation velocities determined from porcine MGG data calculated by each of the four methods.

Figure 9

Magnetic field patterns from (a) the SD, (b) DD and (c) ring dipole configurations at successive time instants. The spatial distribution of field patterns from the ring dipole model is intermediate between the SD and DD models. For (a)-(c), c_min/c_max = [±15, ±2, ±15] pT, respectively.