Estimating the Relationship between Heart Rate and Power Output for ...

Available online at www.sciencedirect.com

ScienceDirect Procedia Engineering 112 (2015) 237 – 243

7th Asia-Pacific Congress on Sports Technology, APCST 2015

Estimating the Relationship between Heart Rate and Power Output for Short Term Cycling Exercises Daniel Meyer*, Carolin Dungs, Veit Senner Technische Universität München, Boltzmannstr. 15, 85747 Garching b. München, Germany

Abstract In this paper, we statistically analyze a dataset of performance diagnostics of 1940 subjects to examine the influence of different physical characteristics on the relationship between heart rate and power output. Five characteristics - the cyclist’s height, weight, age, sex and fitness level – were identified as parameters for the model. Next, we divide the dataset into different subsets according to the statistical analysis and modify formulas found in the literature to estimate the maximum heart rate as well as the maximum power output for each group. Then, we derive formulas from the dataset to estimate the heart rate and power output at the individual anaerobic threshold (IAT) as well as the heart rate at low workload. A linear curve between these points describes the immediate relationship between heart rate and power. We compared the results of the adapted formulas to the results of the original formulas for experimental data of 15 subjects. The adapted formulas show better results in terms of mean absolute error (MAE) and sum of squared residuals (SSR) for estimating the maximum power output, but no improvement in estimating the maximum heart rate. The heart rate at IAT is predicted with a MAE of 9 beats per minute (bpm) and heart rate for low intensity with a MAE of 13 bpm. Power at the IAT is predicted with a MAE of 22 Watts. © 2015 2015The The Authors. Published by Ltd. Elsevier © Authors. Published by Elsevier This isLtd. an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/). Peer-review under responsibility of the School of Aerospace, Mechanical and Manufacturing Engineering, RMIT University. Peer-review under responsibility of the the School of Aerospace, Mechanical and Manufacturing Engineering, RMIT University

Keywords: electric bicycles; power output estimation; heart rate modeling; human physiology

* Corresponding author. Tel.: +49 89 289 10351; fax: +49 89 289 15389. E-mail address: [email protected]

1877-7058 © 2015 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license

(http://creativecommons.org/licenses/by-nc-nd/4.0/). Peer-review under responsibility of the the School of Aerospace, Mechanical and Manufacturing Engineering, RMIT University

doi:10.1016/j.proeng.2015.07.206

238

Daniel Meyer et al. / Procedia Engineering 112 (2015) 237 – 243

1. Introduction Electric bicycles are becoming more important as a mean of transportation, but also as training equipment for people of different ages. The assistance provided by the electric motor successfully reduces the perceived exertion of the cyclist and consequently can prevent over exercising [1]. However, due to battery limitations, the limited range of electric bicycles and the large amount of factors influencing the range, make planning cycling sessions difficult. Accurately estimating the residual range and predicting the necessary motor power for a trip improves the usability of electric bicycles because it reduces the risk of running out of battery. The necessary motor power depends on route and bicycle characteristics, but also to a huge extent on the fitness level of the cyclist (Fig. 1). Estimating the fitness level is therefore crucial for a successful management of the energy provided by the battery as well as the cyclist. The fitness level of a human is very specific to each individual and estimating it precisely is important for optimal training control and training progress. Heart rate, the maximum oxygen uptake or the individual anaerobic threshold are good indicators of fitness level. Different test procedures and equipment already exist for accurate measurement of these parameters [2]. For cyclists, the most accurate analysis is a performance diagnostic on a bicycle ergometer. However, a professional diagnostic implies high costs and requires a laboratory. Modern sport equipment often includes models to estimate the fitness level using individual data like age, sex or the Body-Mass-Index (BMI). This data provides information about the fitness and is easily accessible for recreational cyclists. Still, these models do not achieve the same accuracy as laboratory tests.

Fig. 1. Energy management system and parameters affecting the range of electric bicycles

The relationship between the heart rate and the human performance can be assumed linear, with the gradient depending on the physical condition of the cyclist [3]. According to [4] this linear relationship ends at about 80% of the maximum heart rate, the so-called deflection point, and the curve levels. It is also assumed that the deflection point matches with the individual anaerobic threshold (IAT). The IAT is an indicator for physical capability as it characterizes the type of energy supply in the muscles. Different tables and formulas were already proposed in the literature, to estimate the maximum power output (Pmax) as well as the maximum heart rate (HRmax). The formula recommended in Austria [4] uses the height, weight and age to estimate Pmax. The formulas for men and women are given by:

239


(1) with BS defined as the body surface given by . The formulas proposed by Wassermann [5] consider weight and age to be the determining parameters and are defined as the following: (2) The formulas for Pmax proposed by Jones again consider age, weight and height and are given by: (3) For HRmax a formula depending only on age was proposed in [6] and is given by: (4) These formulas only provide information about the maximum values of heart rate and power output of cyclists. It is assumed that the heart rate at IAT (HRIAT) is located at about 80% of HRmax. No model to estimate the power at the IAT (PIAT) is known to the authors yet. Therefore, different formulas need to be derived in order to model the heart rate response of cyclists to different power outputs and to model the relationship between power output and heart rate. The outline of the paper is as follows: Section 2 describes the methods we used to analyze the dataset and to adapt and derive new formulas for the relationship of the heart rate and power output. In Section 3 the results of the new formulas are presented and compared to the existing formulas as well as experimental results. Section 4 and 5 discusses the results and presents the conclusion of the paper. 2. Methodology We used a dataset of 1940 subjects who performed an incremental progressive cycle ergometer test. Individual data (see Table 1) – age, sex, height, weight and subjective estimate of level of fitness – were taken of each subject before the test was performed. Subjects were able to choose between three fitness levels – 1: untrained, 2: average fitness level and 3: well trained, respectively – to indicate their personal fitness. The starting power for the experiments was set to 25W, 50W or 80W, respectively, and power was increased by 30 W (25 W for untrained subjects) every 3 minutes until the subject was not able to proceed with the test anymore. During the tests the heart rate was measured and a blood sample was drawn after each increment to measure the blood lactate value after every stage. IAT was determined using the Dickhuth-model [7]. For the statistical analysis we classified the participants according to age (1: < 35 years, 2: 35 25

Fitness level

Number of participants

b0,HR

b1,HR

SE

p

R²

F

p

1

276

208

-0.83

0.06

< .001

0.38

170.69

< .001

2

831

206

-0.68

0.03

< .001

0.32

383.92

< .001

3

97

210

-0.72

0.09

< .001

0.39

61.17

< .001

1

188

211

-1.05

0.10

< .001

0.39

119.32

< .001

2

485

204

-0.76

0.06

< .001

0.26

174.04

< .001

3

63

213

-0.85

0.13

< .001

0.39

39.32

< .001

3. Results First, the dependency of HRmax on the individual data was statistically analyzed. The t-Test shows a significant difference between subjects with BMI smaller than 25 and subjects with BMI greater than 25 (t-test p < .001). ANOVA also showed a significant difference between the fitness levels for HRmax (ANOVA p < .001). We used a post-hoc test to check the difference between every fitness level and they all showed a significant difference (level 2 and 3: p = .007; rest p < .001). The sex however is not a significant parameter for HRmax (t-test p = .080). According to this results the dataset was divided into subsets in terms of the BMI and the fitness level. For every subset of data a linear regression with age as the predictor was performed. The formula for linear regression is given by (5). The resulting factors of every subset are given in Table 2. (5) Next, the dependency of Pmax on the individual data was statistically analyzed. According to [6] the maximum human performance depends on age and bodyweight. Our dataset showed significant dependencies concerning sex (t-test: p < .001) and fitness level (ANOVA: p < .001; post hoc test: all groups p < .001). According to this results the dataset was again divided into subsets regarding sex, BMI and fitness level. We used a multiple regression with age and bodyweight as predictors to explain Pmax. The formula for a multiple linear regression with two predictors is given by (6). Table 3 shows the identified parameters for every subset. (6) HRIAT and PIAT as well as HR1 are expressed as a percentage of HRmax and Pmax, respectively, for each subject. Again, the dependency of the values at the IAT on individual data was tested using ANOVA and t-tests. The participants were divided in three age groups (1: < 35, 2: 35>x65), to test the dependency of the parameters on age. For HRIAT and HR1 the tests showed significant difference regarding sex (t-test: p = .001), age (ANOVA: p = .001) and fitness level (ANOVA: p < .001). Post-hoc tests showed a significance between participants older than 65 and those younger than 65 years and between the different fitness levels.

241


Table 3. Results of the multiple regression for groups divided by sex and fitness level to estimate the maximum power Pmax

Sex

m

w

Fitness level

Number of participants

b0,p

b1,p

SE

p

b2,p

SE

p

R²

F

p

1

128

160.86

-1.23

0.26

< .001

0.93

0.27

< .001

0.25

20.33

< .001

2

947

323.98

-1.47

0.12

< .001

-0.13

0.13

< .332

0.13

70.72

< .001

3

158

252.15

-0.96

0.32

< .003

0.96

0.34

< .006

0.09

7.64

< .001

1

336

186.15

-1.19

0.11

< .001

0.21

0.12

< .073

0.25

56.93

< .001

2

369

170.84

-0.82

0.15

< .001

0.66

0.17

< .001

0.10

21.30

< .001

3

2

-

-

-

-

-

-

-

-

-

-

Table 4. Mean absolute errors (MAE) with standard deviations (SD) and sum of squared residuals (SSR) for the new formulas as well as for the formulas found in the literature Parameter Pmax HRmax

New formulas (5-6)

Formula (1)

Formula (2)

Formula (3)

Formula (4)

MAE ± SD

21 ± 20

42 ± 31

48 ± 35

64 ± 35

-

SSR

12522

40187

51690

78161

-

MAE ± SD

10 ± 7

-

-

-

9±7

SSR

2162

-

-

-

1868

Therefore the dataset was divided into subsets regarding sex, age and fitness level and the mean of the percentages of HRIAT was calculated to get a generalized model for predicting HRIAT. For PIAT statistical analysis showed significant differences between the fitness levels (ANOVA: p < .001) and the three age groups (ANOVA: p < .001). According to these results the dataset was again divided into subsets and the mean of all percentages for PIAT was also calculated. Hence, the formulas to estimate HR1, HRIAT and PIAT are defined as follows: (7) (8) (9) For the validation of the adapted formulas, 15 subjects (individual parameters given by Table 1) under 35 years old performed an incremental cycle ergometer test with the same procedure as described in Section 2. The surveyed parameters of the performance diagnostics were the maximum power output (Pmax), the maximum heart rate (HRmax), the power at the individual anaerobic threshold (PIAT) the heart rate at the IAT (HRIAT) and the heart rate after the first increment (HR1). After the test, the measured data were compared to the calculated data of the new formulas as well as the original formulas (1) – (4). Table 4 shows the mean absolute error (MAE) with standard deviation (SD) as well as the sum of squared residuals (SSR) for the estimated data by our formulas and the formulas from the literature when compared to the measured data. Regarding the maximum power output, the proposed adapted formulas show less deviation than the original formulas. In case of the maximum heart rate our model is less accurate for the tested subject group and reevaluating the formula might be necessary. Table 5 shows MAE with SD and SSR for the parameters at the IAT and for the first test increment. The accuracy of these values is similar to the accuracy of the prediction of the maximum values.

242


4. Conclusion In this paper we presented a method to estimate the immediate heart rate response for cycling exercises. We evaluated a dataset of performance diagnostics of 1940 subjects to derive formulas to estimate the maximum power output (Pmax), the maximum heart rate (HRmax), the power at the individual anaerobic threshold (PIAT), the heart rate at IAT (HRIAT) and the heart rate at a low workload (HR1) for subjects with different individual parameters. These points can be used to estimate a linear relationship between power output and heart rate for subjects with different physiological constitution. Table 5. Mean absolute error (MAE) and standard deviation (SD) for the power output and heart rate at the individual anaerobic threshold and the heart rate after the first test increment

PIAT

HRIAT

HR1

MAE ± SD

25 ± 17

12 ± 10

15 ± 9

SSR

13598

3370

4523

The new formulas were validated for subjects with a specific set of individual parameters. The new formulas estimate Pmax with less error for this test group than formulas provided by the literature (MAE of 21 compared to MAE of 42, 48, 64). However, no improvement was achieved for HRmax (MAE of 10 compared to 9). HRIAT and PIAT were estimated with similar error as Pmax and HRmax. Therefore, the heart rate response to a given power output for short exercises can be estimated and the formulas can be used in models to estimate the necessary power output of electric bicycles to perform cycling sessions with different intensity. 5. Discussion The developed formulas were only validated for a small number of subjects and need to be verified for additional subjects to prove the general validity of the formulas. In this paper we use the whole dataset of performance diagnostics for modeling. Another approach could be to divide the dataset in data for modeling and data for cross validation for each subset. Consequently, the modeled formulas could be verified directly, provided that enough subjects remain in each subset. Heart rate and power output at the anaerobic threshold are calculated as a percentage of the maximum values (see equations (7) – (9)). Hence, errors in our model for the maximum values will be added to errors of the models for values at IAT. Using linear regression or multiple regression to derive formulas for HRIAT and PIAT might reduce this error and result in formulas with increased accuracy. Since no improvement for estimating HRmax could be achieved, further analysis of the data is be necessary. HRmax differs almost significantly for the sex of the subjects (p = .080). A classification into men and women might therefore lead to better results and can be performed easily. The self-classification of the participants into three fitness levels might not reflect the real fitness level accurately and could lead to misclassification. Standardized procedures have to be found to classify the subjects more precisely. Since the heart rate is affected by many different parameters, the accuracy of the models for outdoor cycling and varying conditions should be analyzed. Moreover, the formulas do not account for gradual increases in heart rate due to the cardiovascular drift [8]. Future work will include experiments to prove the validity of the model for subjects with different individual parameters as well as varying exercise profiles. In addition, it will include the development of a model to estimate the gradual heart rate response during prolonged exercises due to cardiovascular drift.


Acknowledgements We would like to thank the Department for Prevention, Rehabilitation and Sports Medicine (PRS) of the Technische Universität München (TUM) for conducting the performance diagnostics as well as providing the dataset. References [1] Meyer, D., Steffan, M., Senner, V., Impact of Electrical Assistance on Physiological Parameters During Cycling, Procedia Engineering 72, (2014), 150-155 [2] McArdle, W.D., Katch, F.I.., Katch, V.L., Essentials of Exercise Physiology, Williams and Williams, Baltimore. [3] de Marées, H. (2003). Sportphysiologie. Köln: SPORTVERLAG Strauss [4] Tomasits, D., & Haber, A.-P. (2011). Leistungsphysiologie – Grundlagen für Trainer, Physiotherapeuten und Masseure. Wien: SpringerVerlag. [5] Kroidl, F., Schwarz, S., & Lehnigk, B. (2010). Kursbuch Spiroergometrie – Technik und Befundung verständlich gemacht (2., aktualisierte und erweiterte Auflage Ausg.). Stuttgart: Georg Thieme Verlag [6] Löllgen P., (2005). Kardiopulmonale Funktionsdiagnostik. Nürnberg: Novartis Pharma GmbH [7] Faude, O., Kindermann, W., Meyer, T., Lactate Threshold Concepts: How valid are they?, SportsMedicine, 39(6) (2009) 469-490. [8] Coyle, E., Gonzlez-Alonso, J., Cardiovascular drift during prolonged exercise: new perspectives, Exercise and Sport Sciences Reviews, 29(2) (2001) 88-92.

243