Wave equation based interpolation on volumetric cardiac electrical potentials

Like any measurement involving discrete spatial sampling, mapping of the electrical activity in the heart requires interpolation to estimate the values of electric potential between and around measured values. Interpolation is never perfect but can often perform better using application specific approaches than with general purpose methods and cardiac mapping has motivated a number of such customized interpolation techniques. Wave equation based (WEB) interpolation is one such specialized interpolation technique that has been shown to preserve sharp gradients on surface mapping data within electrograms recording from the heart surface, but has not been applied to volumetric data. The special strength of WEB interpolation is the preservation of sharp spatial gradients and we propose that WEB interpolation will also provide accurate unbiased interpolation of volumetric interpolation over sharp gradients in volumetric cardiac mapping data. We applied WEB interpolation in conjunction with linear and volumetric Laplacian interpolation methods and compared them to the same methods in their non-WEB forms. The basis for comparison were extracellular potentials from a high resolution simulation of cardiac activation. The results for the voltage gradients using the WEB methods were more than 2.6 times more accurate than the non-WEB methods at a very slight cost in accuracy in the regions of low spatial gradient. These results demonstrate that WEB approaches capture intrinsic features in the context of cardiac mapping and can augment and improve the accuracy of other interpolation techniques.