Each heartbeat can be drawn as a point on a sheet of paper. Thousands of these points merge into a cloud. The Mapper algorithm turns this cloud into a network: it connects points that behave similarly and colors them according to blood flow strength. The result is not just a pile of numbers but a colored map showing which parts of the heart work in sync and which are out of step.
In experiments on pigs with weakened hearts, two ways of stimulating the left ventricle were compared: from the outside (epicardial) and from the inside (endocardial). Electrodes were placed in different zones — at the base, in the middle, and at the apex of the heart. For each zone, four blood flow parameters were measured. The algorithm then built graphs and computed three numbers: how tightly the points in the graph cluster together (self-connectivity), how scattered they are (dispersion), and how evenly they fill the space (uniformity).
The results were surprising: the basal regions, those closer to the atria, showed a self-connectivity of 0.57—data points there held together like a flock of birds. The mid regions had only 0.14, and the apex 0.24. The difference is statistically significant. When stimulation was internal, the contrast between the base and other zones became even sharper. This means that internal stimulation of the basal regions gives the most stable and predictable heart response.
Such analysis doesn't just confirm what doctors knew intuitively: it provides a numerical measure. Now different stimulation methods can be compared not by eye but by strict indices. This is a step toward personalized pacemaker tuning: the algorithm will suggest exactly where to place the electrode to make the heart beat more evenly.
as written by the authors arXiv:2604.18634
Objective: The Mapper algorithm is a qualitative method in topological data analysis that constructs graphs from point clouds by combining dimensionality reduction and clustering techniques. The aim of this study is to apply Mapper, together with novel quantitative indices, to compare the effects of biventricular pacing from the left ventricular epicardium versus the endocardium in a swine model of pacing-induced non-ischemic cardiomyopathy. Methods: The distributions of four hemodynamic variables from a previous study on endocardial and epicardial cardiac resynchronization in an experimental swine model of nonischemic cardiomyopathy were analyzed using the Mapper algorithm, enhanced with numerical indices quantifying self-connectivity, scattering, and homogeneity of the resulting colored graphs. Results: Statistically significant differences were observed between pacing from basal regions versus mid or apical regions, with the following self-connectivity index values: basal $$0.57$$; mid $$0.14$$ ($$p < 0.01$$); apical $$0.24$$ ($$p < 0.01$$). Endocardial stimulation at lateral sites increased the contrast between the distributions of basal versus mid or apical data, when compared with epicardial stimulation. Conclusions: Topological analysis using the Mapper algorithm, enhanced with quantitative statistical measures, revealed new and biologically plausible significant differences in pacing effects across heart regions.
A pig's heart is very similar in size and physiology to a human heart, so it is often used for testing pacemakers.