Comparing Heart Rate Models for Characterization of Cardiorespiratory Fitness in Incremental Cycling Exercise: A Preliminary Study

Abstract

Introduction

Recent advances in wearable technologies enable continuous heart rate (HR) recordings during physical activity. Based on the availability of high-frequency HR data, studies have emerged that model HR as a function of power output. These studies argue that the parameters of an individualized HR model are related to an individual’s cardiorespiratory response to exercise and could therefore be leveraged for monitoring fitness. However, the proposed HR models differ in their structure and complexity. The aim of the present study is to compare three HR modeling approaches: the convolution model (CONV; De Leeuw et al., 2023), the polynomial convolution model (CONV-POLY; Ludwig et al., 2019), and the differential equation model (DE; Mongin et al., 2020). These models were chosen because previous studies have hypothesized that each model has one parameter that is associated with fitness. Furthermore, a baseline linear regression model (REG) was considered. The four models were compared by assessing the relationship between their parameters and VO₂peak/kg (a measure of cardiorespiratory fitness) in cycling tests.

Methods

This preliminary analysis included 23 healthy adult males who performed one cardiopulmonary exercise test (CPET) on a cycle ergometer. The HR models were fitted for each test individually, and the Spearman correlation coefficient between the model parameters and the measured VO₂peak was determined.

Results

In both the REG and DE models, the parameter that captures the proportionality between HR and power was significantly correlated with VO₂peak/kg (correlation coefficient  and its 95% confidence interval; REG: =-0.69 [-0.86, -0.39]; DE: =-0.69 [-0.86, -0.40]). No parameter of CONV or CONV-POLY exhibited significant correlations.

Discussion

The negative correlation between VO₂peak and the proportionality parameters is consistent with the fact that a lower HR at a given power may indicate cardiorespiratory fitness improvements. Thus, the proportionality parameters of REG and DE offer a practical and interpretable basis for characterizing and monitoring fitness. By contrast, CONV and CONV-POLY likely underperform because their higher number of parameters leads to less interpretable, multidimensional representations of fitness.

Conclusion

The good results of the baseline REG model raise doubts about whether the higher complexity of the other models is justified for practical application. This is an important consideration, as current studies often overlook the impact of model choice on their results. The preliminary results from the present study motivate further comparisons of HR models, with priority on larger samples, female representation, different demographics and field-based fitness tests.

References

De Leeuw, A.-W., Heijboer, M., Verdonck, T., Knobbe, A., & Latré, S. (2023). Exploiting sensor data in professional road cycling: Personalized data-driven approach for frequent fitness monitoring. Data Mining and Knowledge Discovery, 37(3), 1125–1153. https://doi.org/10.1007/s10618-022-00905-5

Ludwig, M., Grohganz, H. G., & Asteroth, A. (2019). A Convolution Model for Prediction of Physiological Responses to Physical Exercises. In J. Cabri, P. Pezarat-Correia, & J. Vilas-Boas (Eds.), Sport Science Research and Technology Support (pp. 18–35). Springer International Publishing. https://doi.org/10.1007/978-3-030-14526-2_2

Mongin, D., Chabert, C., Uribe Caparros, A., Collado, A., Hermand, E., Hue, O., Alvero Cruz, J. R., & Courvoisier, D. S. (2020). Validity of dynamical analysis to characterize heart rate and oxygen consumption during effort tests. Scientific Reports, 10(1), 12420. https://doi.org/10.1038/s41598-020-69218-1