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The purpose of this study was to demonstrate errors in activation time maps created using the time derivative method on fractionated unipolar electrograms, to characterize the epicardial distribution of those fractionated electrograms, and to investigate spatial methods of activation time determination. Electrograms (EGs) were recorded using uniform grids of electrodes (1 or 2 mm spacing) on the epicardial surface of six normal canine hearts. Activation times were estimated using the time of the minimum time derivative, maximum spatial gradient, and zero Laplacian and compared with the time of arrival of the activation wave front as assessed from a time series of potential maps as the standard. When comparing activation times from the time derivative for the case of epicardial pacing, spatial gradient and Laplacian methods with the standard for EGs without fractionation, correlations were high (R2 = 0.98, 0.98, 0.97, respectively). Similar comparisons using results from only fractionated EGs (R2 = 0.85,0.97,0.95) showed a lower correlation between times from the time derivative method and the standard. The results suggest an advantage of spatial methods over the time derivative method only for the case of epicardial pacing where large numbers of fractionated electrograms are found.

Interpolation plays an important role in analyzing or visualizing any scalar field because it provides a means to estimate field values between measured sites. A specific example is the measurement of the electrical activity of the heart, either on its surface or within the muscle, a technique known as cardiac mapping, which is widely used in research. While three-dimensional measurement of cardiac fields by means of multielectrode needles is relatively common, the interpolation methods used to analyze these measurements have rarely been studied systematically. The present study addressed this need by applying three trivariate techniques to cardiac mapping and evaluating their accuracy in estimating activation times at unmeasured locations. The techniques were tetrahedron-based linear interpolation, Hardy's interpolation, and least-square quadratic approximation. The test conditions included activation times from both high-resolution simulations and measurements from canine experiments. All three techniques performed satisfactorily at measurement spacing < or = 2 mm. At the larger interelectrode spacings typical in cardiac mapping (1 cm), Hardy's interpolation proved superior both in terms of statistical measures and qualitative reconstruction of field details. This paper provides extensive comparisons among the methods and descriptions of expected errors for each method at a variety of sampling intervals and conditions.

In mapping the electrical activity of the heart, interpolation of electric potentials plays two important roles. First, it permits the estimation of potentials in regions that could not be sampled or where signal quality was poor, and second, it supports the construction of isopotential lines and surfaces for visualization. The difficulty in developing robust interpolation techniques for cardiac applications lies in the abrupt change in potential in the vicinity of the activation wave front. Despite the resulting nonlinearities in spatial potential distributions, simple linear interpolation methods are the current standard and the resulting errors due to aliasing can be large if electrode spacing does not lie on the order of 0.5-2 mm--the thickness of the activation wave front. We have developed a novel interpolation method that is based on two observations specific to the spread of excitation in the heart: (1) that propagation velocity changes smoothly within a region large enough to contain several measurement electrodes and (2) that electrogram morphology varies very little in the neighborhood of each sample point except for a time shift in the potential wave forms. The resulting interpolation scheme breaks the interpolation of one highly nonlinear variable--extracellular potential--into two separate interpolations of variables with much less drastic spatial variation--activation time and electrogram morphology. We have applied this method to potentials originally recorded at 1.5 mm spacing and then subsampled at a range of densities for testing of the interpolation. The results based both on reconstruction of isopotential contour maps and statistical comparison showed significant improvement of this novel approach over standard linear techniques. The applications of the new method include improved determination of electrophysiological parameters such as spatial gradients of potential and the path of cardiac activation and recovery, estimation of electrograms at desired locations, and visualization of electric potential distributions.

Mapping of bioelectric potentials over a given surface (e.g., the torso surface, the scalp) often requires interpolation of potentials into regions of missing data. Existing interpolation methods introduce significant errors when interpolating into large regions of high potential gradients, due mostly to their incompatibility with the properties of the three-dimensional (3D) potential field. In this paper, an interpolation method, inverse-forward (IF) interpolation, was developed to be consistent with Laplace's equation that governs the 3D field in the volume conductor bounded by the mapped surface. This method is evaluated in an experimental heart-torso preparation in the context of electrocardiographic body surface potential mapping. Results demonstrate that IF interpolation is able to recreate major potential features such as a potential minimum and high potential gradients within a large region of missing data. Other commonly used interpolation methods failed to reconstruct major potential features or preserve high potential gradients. An example of IF interpolation with patient data is provided to illustrate its applicability in the actual clinical setting. Application of IF interpolation in the context of noninvasive reconstruction of epicardial potentials (the "inverse problem") is also examined.