Cross-validation of Fox and Tanaka equations in predicting maximal heart rate of Iranian Children and Adolescent boys: Evaluation by the respiratory gas analyzer method in the exhaustive exercise test

Document Type : Original Article


Department of Sport Physiology, Faculty of Sports Sciences, Bu-Ali Sina University, Hamedan, Iran


Background and Purpose: The maximal heart rate is a physiological index to control the intensity of physical activity in exercise and rehabilitation. Due to the practical problems of measuring maximal heart rate in strenuous exercise tests, this physiological index is estimated by regression equations. Most scientific sources have used the two equations of Fox (age - 220) and Tanka (208 -0.7 age) to estimate the maximal heart rate. Fox and Tanaka's equations were designed based on the data obtained from the adult population. Therefore, these two equations may not be highly accurate in the child and adolescent population. The purpose of this research is to evaluate the validity of Fox and Tanaka's equations in estimating the maximal heart rate of children and adolescent boys.
Materials and Methods: In the present study, maximal heart rate was measured in 349 healthy boys aged 8 to 18 years in a direct method by using modified Bruce test on a treadmill equipped with a respiratory gas analyzer. Thereafter, the maximal heart rate was estimated using Fox and Tanaka’s equations. In order to validate the equations of Fox and Tanaka, the measured and estimated maximal heart rate were compared in all subjects as well as children and adolescent. For this purpose, Pearson's correlation, pair sample t-test, and Bland-Altman's agreements were used.
Results: With increasing the age of the subjects, there was no noticeable change in the maximal heart rate of the boys. So that, a weak negative correlation was observed between age and maximal heart rate (r = -0.198, p<0.05). A significant correlation was observed between the maximal heart rate measured by the standard method with Fox (r=0.198) and Tanaka (r=0.198) equations (P<0.05). However, there was a significant difference between the measured maximal heart rate and estimated maximal heart rate by Fox (mean difference = 5.23±6.32, equivalent to 2.7% of the mean for maximal heart rate) and Tanaka (mean difference = 3.07±6.17, equivalent to -1.44 percent of mean for measured maximal heart rate). The Fox and Tanaka equations led to overestimation and underestimation of maximal heart rate, respectively. Furthermore, the Bland-Altman diagram indicated a low agreement between the maximal heart rate equations of Fox and Tanaka compared to the standard method. Even by dividing the subjects into two age groups, 8 to 13 years and 14 to 18 years, no changes in the results were found. No significant correlation was observed between maximal heart rate of Fox and Tanaka equations with standard method (r = 0.028-0.094) (p<0.05). In addition, a significant (P<0.05) difference was observed between the standard maximal heart rate and the Fox and Tanaka equations (mean difference = - 3.55 to 6.26 beats per minute).
Conclusions: It seems that the Fox and Tanaka heart rate equations do not have sufficient validity in children and adolescent boys. However, in situations where we have to estimate the maximal heart rate, Tanaka's equation has a lower estimation error. According to the results of this research, it will be beneficial to design a native equation for estimating the maximal heart rate of Iranian children and adolescent boys.


Main Subjects

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  • Receive Date: 05 August 2023
  • Revise Date: 29 September 2023
  • Accept Date: 06 November 2023
  • First Publish Date: 22 November 2023
  • Publish Date: 21 January 2024