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Heart rate (HR) is an important indicator of work intensity during physical activity. Maximum heart rate (MHR) is a physiological measure that is frequently used as a benchmark for maximal exercise intensity. The aim of this study was to establish reference curves for maximum heart rate (MHR) and resting heart rate (RHR) and to develop an estimated equation for Tunisian adolescent footballers. The study involved 801 adolescent players, aged 11 to 18, who belonged to five Tunisian first-division soccer teams. The LMS method was used for smoothing the curves and the multivariate linear regression to develop a prediction equation of MHR. Our results showed that MHR and RHR reference curves decrease with age. The values of the median curves of MHR and RHR ranged from 208.64 bpm (11 years) to 196.93 (18 years) and 73.86 (11 years) to 63.64 (18 years), respectively. The prediction equation obtained from the model was MHR= 225.08 - 1.55 X Age (years) (R^{2 }= 0.317; P < 0.001; standard error of the estimate (SEE) = 5.22). The comparisons between the estimated values and the measured values have found that our model (- 0.004 ±5.22 bpm) was to be more accurate than two other widely known models. BOX's equation underestimates the measured MHR values by -3.17 ± 5.37 bpm and TANAKA's equation overestimates by + 4.33 ±5.5 bpm. The reference curves can be used by coaches and physical trainers to classify the resting heart rate (RHR) and maximum heart rate (MHR) of each adolescent player, track their evolution over time, and design tailored training programs with specific intensities for Tunisian soccer players.

The maximum heart rate (MHR) is the highest heart rate achieved during a graded exercise performed at maximum effort, and it can be measured in the laboratory or in the field. MHR determines the upper limit of cardiovascular function (Mahon et al., 2010[_{2}) in activities with progressive intensity (da Silva et al., 2021[_{2}max at a particular effort intensity. Therefore, we can supervise the HR in % MHR and control the intensity of a given physical activity, thus personalized the physical training (Antonacci et al., 2007[

Coaches and physical trainers in soccer frequently base training HR intensities on MHR, and that in cases where direct measurement of MHR is not possible, an equation based on age can be used to predict MHR. FOX's equation (MHR = 220 - age) (Fox et al., 1971[

Reference percentile curves are widely used in medical practice as a screening tool during the important period of childhood. They identify abnormal subjects, in the sense that their value of a given measure is located in one or the other tail of the reference distribution (Borghi et al., 2006[

During the last decades, several countries have established their references or models of physical and physiological parameters in the fields of health and physical activity of trained or untrained subjects (Eytan et al., 2017[

In the pre-season of 2022/2023, we collected a cross-sectional data from 801 football players aged 11 to 18. The subjects are males and were recruited from nine teams in national first division in Tunisia. The participants had regularly participated in at least three training sessions per week and in competitions recognized by the Tunisian Football Federation.

The players voluntarily participated, and they have possibility of leaving the study at any time without justification. They informed their parents of the methods and objectives used to assess their abilities.

In accordance with the Declaration of Helsinki (2013), the research has been fully approved by the Ethics Committee of the Higher Institute of Physical Education and Sports in Kef (22-2023).

Height, body mass and skinfolds were measured using precise tools, including electronic scale to the nearest 0.1 kg (HD-351; Tanita, Arlington Heights, Illinois, USA), portable stadiometer to the nearest 0.001 m (SECA Leicester, United Kingdom) and caliper to the nearest 0.5 mm (Harpenden, West Sussex, UK).

Body mass index was calculated by the ratio of body mass (kg) to square height (m²), and body fat (BF) was estimated from the sum of 4 skinfolds (Triceps, Biceps, Subscapular Suprailiac) using Durnin and Womersley (1974[

where BF is the estimated body fat percentage and D is the density of the body, which is calculated using the sum of the four skinfolds (in millimeters) according to the equation:

The participants performed a running test between two lines separated by 20 meters following the signal of an emitted audio. The initial speed was 8.5 km/h and increased by 0.5 km/h at each one-minute stage (Léger et al., 1988[

The lambda, mu and sigma (LMS) method describes the distribution of the different measurements in the reference percentile curves by three curves: the median, the coefficient of variation and the asymmetry curves (Cole, 1990[

The percentile curves were developed using the following equation:

_{100α}_{α}

Data analyses were performed using the Statistical Package for the Social Sciences (SPSS, version 28.0). Data are presented as means and standard deviations (SD) for all measured variables. Relationships between MHR and continuous variables (weight, height, BMI, body fat percentage, RHR) were provided using Pearson's correlation coefficient. One-way analysis of variance (ANOVA) and subsequent Bonferroni post-hoc test (if differences between groups were revealed) were used to examine differences between successive age group values. In addition, the stepwise method of multivariate linear regression was used to identify predictors of MHR after checking the regression hypotheses (homoscedasticity, multicollinearity, and normal distribution of residuals). Root Mean Squared Error (RMSE) was used to assess the goodness-of-fit of the model. Examination of the accuracy and the variability of the prediction equations was performed by the analysis of Bland, Altman graphical method (Altman and Bland, 1983[

The descriptive characteristics of the sample are presented in Table 1

The sample was distributed over the eight age groups as follows: 12.23 % (11 years), 10.61 % (12 years), 13.61 % (13 years), 13.48 % (14 years), 13.11 % (15 years), 12.86 % (16 years), 10.99 % (17 years) and 13.11 % (18 years). There were significant differences between all successive age groups in terms of height, body mass, and trainability. However, the differences were particularly noticeable for a certain age group in other variables. For BF %, there were significant differences between the 11/12 years (p<0.001), 13/14 years (p<0.0001), and 16/17 years (p<0.01) age groups. For MHR, there were significant differences between the 11/12 years (p<0.001), 14/15 Years (p<0.01), and 17/18 years (p<0.001) age groups. For RHR, there was a significant difference only between the 11/12 years (p<0.001) age group (Table 1

The median curve values for MHR and RHR vary from 208.64 bpm (11 years) to 196.93 bpm (18 years) and from 73.86 bpm (11 years) to 63.64 bpm (18 years), respectively. The lower percentile values (P3) decrease from 196.83 bpm (11 years) to 187.23 bpm (18 years) for MHR, and from 62.59 bpm (11 years) to 51.94 bpm (18 years) for RHR. Similarly, the upper percentile values (P97) decrease from 218.81 bpm (11 years) to 208.10 bpm (18 years) for MHR, and from 84.52 bpm (11 years) to 77.44 bpm (18 years) for RHR (Table 2

The Pearson correlation coefficients between the MHR and the different variables (age, trainability, Body mass, height, BMI, Fat mass percent, RHR) are presented in Table 3

Multivariate linear regression identified two models for production MHR. The first model included age as the only significant predictor using the following prediction equation:

(R^{2} = 0.317, P <, 0.001, standard error of the estimate (SEE) = 5.22).

The error range for this model was -22.47 to +13.66 bpm. The mean difference between the measured and predicted MHR using this equation was -0.004 with a standard deviation of 5.22 bpm.

The second model revealed that both age and BMI were significant predictors of MHR

(R^{2} = 0.324, P < 0.001, standard error of the estimate (SEE) = 5.20.

The error range of second model was -21.95 to +14.62 bpm. The mean difference was -0.066 with a standard deviation of 5.19 bpm.

The two developed models had similar percentages of estimated variation in MHR (31.7 % vs. 32.4 %) and SEE values (5.22 vs. 5.20 bpm). As result, we chose the first equation as the predictor of MHR values for young Tunisian soccer players because it only relied on one variable, which was age.

Figure 3

Bland and Altman graph shows the high degree of agreement between our model 1 and the measured MHR values. Our model 1 demonstrated near-zero bias (+0.003) and upper and lower limits of agreement of +10.23 bpm and -10.24 bpm, respectively (see Figure 4

For the FOX’s and TANAKA’s equations, the Bland and Atman graph illustrated that the biases are not negligible, with values of -3.17 bpm and +4.33 bpm, respectively. The upper and lower limits of agreement for the FOX’s equation are -7.35/+13.70 bpm, and for the TANAKA’s equation they are -15.25/+6.60 bpm (see Figure 4

See also the Supplementary data.

The aim of this study was to develop reference curves of MHR and RHR and produce an estimated equation for children and adolescents' soccer players.

The 3^{rd}, 50^{th}, and 95^{th }percentile values of MHR showed a continuous decrease with age, through variation of decline of around 1.67 ± 0.30 bpm, 1.37 ± 0.72 bpm, and 1.53 ± 0.62 bpm per year, respectively, resulting in an overall decline rate of -4.88 %, -5.61 %, and -4.89 % between the ages of 11 and 18 years. Tanaka et al. (2001[

Smoothed percentile values for RHR are also inversely associated with age. Indeed, the values for the 3^{rd}, 50^{th}, and 97^{th} percentiles vary by 1.52 ± 0.72 bpm, 1.46 ± 0.75 bpm, and 1.01 ± 0.62 bpm per year, respectively, with a total percentage decrease of -17.01 %, -13.84 %, and -8.38 % from 11 to 18 years of age. In the same context, Zanuto et al. (2020[

In a meta-analysis review, Pieles and Stuart (2020[

Zanuto et al. (2020[

Several variables, including anthropometric parameters, age, trainability, and RHR variables, were examined to identify the best predictor of MHR. Our analysis revealed that age is the most significant predictor, with an inverse correlation of -0.56 (p<0.001) with MHR. Previous studies have shown varying degrees of correlation between MHR and age across different age groups of athletes. For example, a correlation coefficient of -0.41 (p<0.001) was reported for soccer players aged 11-36 years (Nikolaidis, 2015[

After analyzing the difference between observed MHR values of young Tunisian soccer players and the predicted values using our model 1, as well as the BOX's equation and TANAKA's equation, we observed biases and standard deviations of -0.003 ± 5.22, -3.17 ± 5.37, and +4.33 ± 5.57, respectively. The errors that exceed the limits of agreement can reach up to 3.6 % for our model 1, 4.8 % for the BOX's equation, and 5.4 % for TANAKA's equation. Our findings align with previous research by Gellish et al. (2007[

Numerous authors have attempted to develop alternative formulas for predicting MHR, but the resulting equations may not be applicable to the general population due to various factors, such as the sample size, age group, and type of stress test (Magrì et al., 2022[

Our study has several strengths. (1) We developed reference values for MHR and RHR that allow for ranking players according to their aerobic capacity compared to those of subjects of the same age and from the same population. (2) We included several parameters, such as age, stature, body mass, BMI, percentage of body fat, trainability, and RHR, as possible predictors for MHR in young Tunisian footballers. (3) We developed first prediction equation for MHR during the adolescent period. However, our study also has some limitations. For instance, the equation we developed only has a 30 % predictive capacity and is applicable to a little age group of 11-18 years. Therefore, future studies should expand the age group by combining the period of adolescence with that of young adult footballers. Additionally, longitudinal studies would be beneficial to better specify the tendencies of the curves of references over time.

Based on these results, it is suggested that the reference curves developed from the Tunisian children and adolescent sample can be used to classify RHR and MHR of each player and to monitor their changes over time. In the context of testing and training, practitioners are advised to use the prediction equation developed in this study, which is more accurate than BOX's and TANAKA's equations. Finally, the reliability of the tools developed in this study needs to be tested by Tunisian coaches and physical trainers.

*: P< 0.01; **: P< 0.001; ***: P< 0.0001; differences between successive age group values