An Analytical Model for the Effects of the Spatial Resolution of Electrode Systems on the Spectrum of Cardiac Signals

It has been suggested that the spatiotemporal characteristics of complex cardiac arrhythmias can be extracted from the spectrum of cardiac signals. However, the analysis of simple bioelectric models indicates that the spectrum of cardiac signals can be affected by the spatial resolution of the electrode system. In this paper, we derive exact measurement transfer functions relating the spectrum of cardiac signals to the spatiotemporal dynamics of cardiac sources. The analysis of the measurement transfer bandwidths for dynamics with different degrees of spatiotemporal correlation shows that as the spatial resolution decreases, the bandwidth of the measurement transfer function decreases until it reaches a constant value. Moreover, this transition from decreasing to constant values is determined by the degree of spatiotemporal correlation of the underlying cardiac source. Motivated by our analytical results, we investigate in a realistic computer simulation environment the impact of additive noise on the accuracy of body-surface dominant frequency (DF) maps. Our simulation results show that meaningful DF values are obtained on those locations where the analytical measurement transfer bandwidth is wide. These findings suggest that the accuracy of body-surface DF maps can be limited by the low spatial resolution of body-surface electrode systems.