A new method for non-uniform interpolation of electroanatomical cardiac maps from Cardiac Navigation Systems (CNS) is here proposed and benchmarked. We adapted the equations of support vector machines for estimation problems in terms of the two angular dimensions azimuth and elevation and used an autocorrelation kernel. Moreover, the influence of the number of spatial locations, its minimum number to obtain a map that precisely replicates the original or gold-standard and the effect of working in 2D from 3D were also studied. Two basic simulation scenarios were used: (a) a prolate semi-ellipsoid, yielding a geometry similar to the ventricular chamber, with different width pulse and Gaussian activations; and (b) detailed simulated models of cardiac activity in the atria. Results were compared with those obtained with other interpolation methods. In the Gaussian and pulse-like activations the largest decrease in mean absolute error (MAE) for the test set was achieved by using 150 spatial locations (MAE from 0.007 to 0.117). In the simulation models the error stabilized at 500 spatial locations (MAE from 0,002 to 0.014). The proposed method can provide improved quality for electro-anatomical maps interpolation.
IntroductionArrhythmias are alterations of normal cardiac rhythm, which cause the heart to abnormally beat too fast, too slow, or with an irregular rhythm [1]. Cardiac Navigation Systems (CNS) allow replicating the patient cardiac anatomy in a computer system, addressing catheters precisely within the heart, and registering the cardiac electrical activity. The integration of both anatomical and electric data compounds electro-anatomical maps of the cardiac chamber, in which a compromise between map quality and its acquisition time is required. Given that the electrical feature is measured only in a few spatial locations, an interpolation algorithm is needed to estimate the feature value at points with no measure and build the map from those samples. Precision in the diagnosis and treatment of arrhythmias using CNS is directly related to the quality of the map, and hence to the interpolation method to be considered [2].In this work, a Support Vector Machine (SVM) algorithm with autocorrelation (AC) kernel has been chosen as interpolation method because of its promising results versus other interpolation methods in the presence of nonuniform data [2]. The effect of working in 2D is also studied, and compared to 3D Cartesian coordinates of the spatial locations, so that the corresponding values of an electrical feature measured on those 3D spatial locations were transformed to spherical coordinates and then the radius coordinate was discarded.The data used to evaluate the algorithm under study are a set of four simple features over the surface of a prolate semiellipsoid and some activation time maps obtained from two simulations which replicate the structure of maps generated by a CNS.The paper is organized as follows. Section 2 contains the details of the SVM interpolation algorithm considered. In Sect...