A field-compatible method for interpolating biopotentials

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.