Sample Entropy Analysis Of Ramp Type Cardiopulmonary Exercise Testing

Cardiopulmonary exercise testing (CPET) is increasingly used in clinical evaluation of a wide range of diseases and as a critical tool in health research. Advances in computing and information theory now permit innovation in the analytics of the rich breath-by-breath gas exchange and heart rate (HR) data generated during CPET. We wondered if sample entropy (SampEn) was suitable to explore the dynamic complexity of these signals. Challenges to SampEn analytics in CPET include non-stationarity and short signal durations. In this study, we focused on the typical N ∈ [50, 200] observations in a 10-12 min test. PURPOSE: Examine a novel algorithmic approach to enhance the reliability of entropy physiologic analysis obtained during CPET. METHODS: For signals with N ≤ 200 observations, we addressed SampEn's sensitivity to parameter selection by developing a Bayesian optimization algorithm which balanced the bias-variance tradeoff while simultaneously determining suitable SampEn values with uncertainty bounds. We introduced the Python package "EristroPy," facilitating state-of-the-art analysis and encouraging adherence to best practices and interoperability for practitioners and researchers alike. RESULTS: We validated our SampEn pipeline using both synthetic signals and real-world CPET data from 89 healthy early- and late-pubertal children. For synthetic signals (N ∈ {50, 100, 200}), our approach outperformed the state-of-the-art with significantly lower SampEn variance estimation error (60-90%) and overall SampEn estimation error (9-29%), while ensuring statistical stationarity with the EristroPy framework. Analyzing HR SampEn pre- and post-ventilatory threshold (VT), we observed a 70-80% reduction post-VT (p ≤ 0.00025). HR SampEn was 40-50% lower pre-VT and 83-89% lower post-VT compared to gas exchange metrics. Furthermore, early-pubertal males had significantly lower SampEn HR than early-pubertal females, with 13.29 ± 7.29% decreases (p=0.04) pre-VT and 22.88 ± 10.44% (p=0.02) post-VT. CONCLUSIONS: Our algorithmic advancements offer a fresh perspective for analyzing CPET data via entropy analysis. This approach may expand our ability to explore the underlying physiological mechanisms that govern the responses to physical stress induced by exercise generated in a widely used CPET construct. The work reported in this paper was partially supported by a grant, Award UL1TR003015, from the National Center for Advancing Translational Science of the National Institutes of Health. It was also supported by UC Irvine CTSA UL1TR001414 and Project REACH U01 TR002004