Three-dimensional activation mapping in ventricular muscle: interpolation and approximation of activation times

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.