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Exponential hyperbolic sine function fitting of heart rate response to constant load exercise.
J Mizuo1, T Nakatsu, T Murakami
1Department of Internal Medicine I, Faculty of Medicine, Okayama University Medical School, Okayama, 700-8558 Japan.
The Japanese Journal of Physiology
|November 18, 2000
Summary
The exponential hyperbolic sine function accurately models heart rate (HR) changes during exercise of varying intensities. This mathematical model offers a superior fit compared to traditional exponential curves, especially for low-intensity exercise.
Area of Science:
- Exercise Physiology
- Biomathematics
- Cardiovascular Response
Background:
- Heart rate (HR) response to exercise is a key indicator of cardiovascular function.
- Accurate mathematical modeling of HR dynamics is crucial for understanding exercise physiology.
- Existing models may not adequately capture HR responses across all exercise intensities.
Purpose of the Study:
- To evaluate the efficacy of an exponential hyperbolic sine function in modeling exercise-induced heart rate changes.
- To compare the fitting accuracy of the exponential hyperbolic sine function against traditional exponential curves.
- To determine the optimal mathematical model for analyzing heart rate responses across different exercise loads.
Main Methods:
- Seven healthy male volunteers participated in the study.
- Participants performed constant-load exercise at low (30 W), moderate (75 W), and high (125 W) intensities on a bicycle ergometer.
- Heart rate data were fitted to an exponential hyperbolic sine curve and compared with first- and second-order exponential curves using the least-squares method.
Main Results:
- The exponential hyperbolic sine function provided an adequate fit for HR responses across all exercise intensities (low: r=0.68, moderate: r=0.93, high: r=0.97).
- First-order exponential curves only fitted moderate load responses, while second-order curves did not fit low-load responses effectively.
- The exponential hyperbolic sine function demonstrated a significantly smaller sum of power of residuals for low-load exercise compared to exponential models.
Conclusions:
- The exponential hyperbolic sine function is a robust and useful tool for the quantitative analysis of heart rate responses to exercise across a spectrum of intensities.
- This model offers improved accuracy, particularly for low-intensity exercise, where traditional exponential models show limitations.
- The findings support the application of this advanced mathematical function in exercise physiology research and clinical assessments.