# Dynamical systems and fractal geometry applied to cardiac dynamics analysis in the Peruvian population

## TL;DR

This study uses dynamical systems and fractal geometry to improve cardiac risk assessment for the Peruvian population.

## Contribution

Applies dynamical systems and fractal geometry to adjust diagnostic thresholds for arrhythmias in a Peruvian population.

## Key findings

- Adjusted thresholds improved specificity and accuracy but reduced sensitivity for arrhythmia detection.
- Cohen's Kappa showed fair agreement between the method and conventional diagnosis after threshold adjustment.
- The method demonstrated potential for better alignment with standard diagnoses in the Peruvian population.

## Abstract

Cardiovascular diseases in Peru are a significant public health problem, and effective methods for risk stratification are needed. Using dynamical systems and fractal geometry shows promising results in other populations.

To adjust the limits between normality and disease in diagnoses according to the characteristics of the Peruvian population, using a methodology based on dynamical systems and fractal geometry.

Heart rate and beats per hour were recorded over 24 h in 272 cases, 193 normal and 79 with arrhythmias, from Holter studies. Spatial occupation of attractors and their fractal dimensions were measured to determine its mathematical state. Results were compared using Cohen's Kappa coefficient with respect to conventional diagnosis. The limits of normality and disease were adjusted to improve concordance with the standard for the Peruvian population.

With the original limits, sensitivity was 0.595, specificity was 0.653, positive predictive value was 0.412, negative predictive value was 0.797, and accuracy was 0.636. The Kappa for the 2 × 2 table was 0.219 (95% CI, 0.104–0.334) and for the 3 × 3 table, it was 0.141 (95% CI, 0.050–0.221). By adjusting the limits, sensibility was 0.430, specificity was 0.839, positive predictive value was 0.523, negative predictive value was 0.783, and accuracy was 0.721. The Kappa for the 2 × 2 table was 0.285 (95% CI, 0.164–0.409) and for the 3 × 3, 0.123 (95% CI, 0.036–0.209).

The agreement of the method improved with the new limits, demonstrating a fair level of alignment, characterized by enhanced specificity but reduced sensitivity. More studies are needed for clinical application.