Predicting Heart Rate at the Anaerobic Threshold Using a Machine Learning Model Based on a Large-Scale Population Dataset

Abstract

Background/Objectives: For effective exercise prescription for patients with cardiovascular disease, it is important to determine the target heart rate at the level of the anaerobic threshold (AT-HR). The AT-HR is mainly determined by cardiopulmonary exercise testing (CPET). The aim of this study is to develop a machine learning (ML) model to predict the AT-HR solely from non-exercise clinical features. Methods: From consecutive 21,482 cases of CPET between 2 February 2008 and 1 December 2021, an appropriate subset was selected to train our ML model. Data consisted of 78 features, including age, sex, anthropometry, clinical diagnosis, cardiovascular risk factors, vital signs, blood tests, and echocardiography. We predicted the AT-HR using a ML method called gradient boosting, along with a rank of each feature in terms of its contribution to AT-HR prediction. The accuracy was evaluated by comparing the predicted AT-HR with the target HRs from guideline-recommended equations in terms of the mean absolute error (MAE). Results: A total of 8228 participants included healthy individuals and patients with cardiovascular disease and were 62 ± 15 years in mean age (69% male). The MAE of the AT-HR by the ML-based model was 7.7 ± 0.2 bpm, which was significantly smaller than those of the guideline-recommended equations; the results using Karvonen formulas with the coefficients 0.7 and 0.4 were 34.5 ± 0.3 bpm and 11.9 ± 0.2 bpm, respectively, and the results using simpler formulas, rest HR + 10 and +20 bpm, were 15.9 ± 0.3 and 9.7 ± 0.2 bpm, respectively. The feature ranking method revealed that the features that make a significant contribution to AT-HR prediction include the resting heart rate, age, N-terminal pro-brain natriuretic peptide (NT-proBNP), resting systolic blood pressure, highly sensitive C-reactive protein (hsCRP), cardiovascular disease diagnosis, and β-blockers, in that order. Prediction accuracy with the top 10 to 20 features was comparable to that with all features. Conclusions: An accurate prediction model of the AT-HR from non-exercise clinical features was proposed. We expect that it will facilitate performing cardiac rehabilitation. The feature selection technique newly unveiled some major determinants of AT-HR, such as NT-proBNP and hsCRP.

Keywords: cardiac rehabilitation; feature selection; gradient boosting; machine learning; target exercise heart rate.

Figure 1

Flowchart of patient enrollment. From 2008 to 2021, a total of 21,491 CPETs were carried out. Among these, 10,915 were follow-up CPETs and 8228 were first-time CPETs for each patient. CPET: cardiopulmonary exercise testing.

Figure 2

Predicted AT-HR and its accuracy. Comparison of the mean absolute errors (MAE) in predicting AT-HR using the Karvonen formula (coefficient, k = 0.7) (A), the Karvonen formula (coefficient, k = 0.4) (B), Resting HR + 10 (C), Resting HR + 20 (D), and machine learning model (E). (F) shows the relationship between the number of used features and the accuracy of the AT-HR prediction. The test curve (in red) shows that MAE decreases at first as the number of features increases, but after about 20 features, the decrease in errors plateaus. MAE: mean absolute error; AT-HR: anaerobic threshold heart rate.

Figure 3

Impact of our machine-learning-based multi-factor AT-HR estimation. The model is trained with a CPET data set comprising a diverse cross-sectional cohort. Once trained, the model can predict individual AT-HR from various patient characteristics without actual CPET, allowing the patients to exercise with the knowledge of their AT-HR levels. CPET: cardiopulmonary exercise testing; AT-HR: anaerobic threshold heart rate.