Topological analysis of hemodynamic response to cardiac resynchronization therapy

The Mapper algorithm is a qualitative method in topological data analysis that constructs graphs from point clouds by combining dimensionality reduction and clustering. We apply Mapper, together with quantitative graph indices proposed in this work, to compare the effects of left ventricular epicardial and endocardial biventricular pacing in a swine model of pacing-induced non-ischemic cardiomyopathy. Distributions of four hemodynamic variables from a previous study were analyzed using Mapper, complemented by numerical indices quantifying self-connectivity, scattering, and homogeneity of the resulting graphs. Statistically significant differences were observed among basal, mid, and apical pacing regions, with self-connectivity index values of 0.62 (basal), 0.29 (mid), and 0.21 (apical), and with p < 0.05 for both basal-versus-mid and basal-vs.-apical comparisons. Moreover, endocardial stimulation at lateral sites increased the contrast between basal and mid or apical distributions compared with epicardial stimulation. These findings indicate that the proposed graph indices extend Mapper from a qualitative visualization tool to a quantitative framework for comparing pacing-induced hemodynamic distributions.