A Convolution Model for Heart Rate Prediction in Physical Exercises: - PDF document

See discussions, stats, and author profiles for this publication at: https://www.researchgate.net/publication/309910919 A Convolution Model for Heart Rate Prediction in Physical Exercises: Presentation Slides Presentation · November 2016 CITATIONS READS 0 32 1 author: Melanie Ludwig Hochschule Bonn-Rhein-Sieg 13 PUBLICATIONS 47 CITATIONS SEE PROFILE Some of the authors of this publication are also working on these related projects: S.W.E.A.T. for Science View project eTa: efficient transportation alternatives View project All content following this page was uploaded by Melanie Ludwig on 11 November 2016. The user has requested enhancement of the downloaded file.

A Convolution Model for Heart Rate Prediction in Physical Exercise Melanie Ludwig , Harald G. Grohganz, Alexander Asteroth

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Wha hat is is he hear art rat ate e mod odelling elling? 4

Heart Rate Modelling Input Model Output Parameter 5

Heart Rate Modelling Wattage 𝑣 Model Heart rate 𝑧 𝑢 ≔ ℳ Ԧ 𝑏, 𝑣 Parameter 𝑏 Ԧ Optimized with measured heart rates from previous trainings 6

Requirement: Heart Rate Prediction Simulation 7

How ow to to us use he heart art rat ate e models odels?

Usually … HR [bpm] to predict time [s] measured HR time horizon

Now … HR [bpm] to predict time [s] measured HR time horizon

Heart Rate Prediction Models • Usually [e.g.: 1, 2]: o Predicting some seconds into the future o Used for (automatic) control systems • Applicability for complete HR curve prediction? • Preceding study: comparement of literature models o Best results for Takagi-Sugeno model and LTI model [3] [1] Cheng et al. (2007), [2] Mohammad et al. (2011) , [3] Ludwig et al. (2015) 11

Can Can we we us use he hear art rat ate e models odels to pr to predict edict a a com omplete plete he hear art rat ate e cur urve ve? 12

Example: LTI Model LTI model: Cheng et al. (2007) 13

Example: Takagi-Sugeno Model TS model: Mohammad et al. (2011) 14

Example: Takagi-Sugeno Model Strongly dependent on the data and the way of parameter fitting  Overfitting? TS model: Mohammad et al. (2011) 15

The Convolution Model 16

How ow can an we we pr predic edict a a com omplete plete he hear art rat ate e cur urve ve?

Convolution Model 𝒃 𝟓 + 𝒃 𝟒 1 𝒃 𝟐 ⋅ 𝑣 ∗𝑓 Τ ∙ 𝒃 𝟐 𝑧 𝑢 = 𝒃 𝟑 ⋅ 𝑢 • 𝑏 1 : memory parameter • 𝑏 2 : impact parameter • 𝑏 3 : level parameter • 𝑏 4 : slope parameter 18

Data • Three male cyclists (non-professional) • Standardized step size protocol every 2-4 weeks 19

Data • 4+5+8 data sets  30 prediction experiments o fitting on at least 2 training sessions # data sets Fitting on … Prediction on … # of prediction experiments 2 4 (subj. #3) <1,2>; <1,2,3> 3,4; 4 ෍ 𝑗 = 3 𝑗=1 3 5 (subj. #1) <1,2>; <1,2,3>; <1,2,3,4> 3,4,5; 4,5; 5 ෍ 𝑗 = 6 𝑗=1 6 8 (subj. #2) <1,2>; <1,2,3>; …; <1,2,3,4,5,6,7> 3,…,8; 4,…,8; … ; 7,8; 8 ෍ 𝑗 = 21 𝑗=1 20

First Competitiveness 21

En Enha hancement ncement: Are e these hese pa parameters ameters sui uitable table for or mod odelling elling fit itne ness ss ? ?

Parameter Reduction 𝑏 4 + 𝑏 3 1 𝑏 1 ⋅ 𝑣 ∗𝑓 Τ ∙ 𝑏 1 𝑧 𝑢 = 𝑏 2 ⋅ 𝑢 • RMSE for 4 parameter model: 9.25 bpm • Two experiments yields best results: 1. Fixed level parameter to resting heart rate (6.12 bpm) 2. Fixed level parameter 𝑏 3 to resting heart rate, fixed exponential parameter 𝑏 4 to 0.9, polynomial linkage of parameter 𝑏 1 and 𝑏 2 (6.31 bpm) 23

Reduced Convolution Model 0.9 1 𝑏 1 ⋅ 𝑣 ∗𝑓 Τ ∙ 𝑏 1 𝑧 𝑢 = 𝜷 ⋅ + HR rest 𝑢 with 𝑏 1 = 2.06 + 158.8 ⋅ 𝜷 − 36750 ⋅ 𝜷 2 24

Parameter Reduction 25

Correlation: 𝛽 and fitness? Completely untrained before Christmas break in training Form on the day? 26

Correlation: 𝛽 and fitness? 27

Next ext steps eps?

Future Work • Accuracy in outdoor cycling • Accuracy in other sports (esp. one parameter model) o First results for two running athletes 29

Future Work • Validation of a possible correlation between 𝛽 and the subject‘s fitness o More subjects o Evaluation with professional athletes for better benchmark  Correlation with Lactate / maxLASS? 30

Conclusion • Difficult to use existing heart rate models for prediction o Often too many parameters (unstable) • Convolution Model for predicting a whole heart rate curve o Low errors around 6 bpm • Huge reduction of complexity: using only one parameter (might indicate fitness!) !? 31

References • Cheng et al. (2007): Cheng, T. M., Savkin, A. V., Celler, B. G., Wang, L., and Su, S. W. (2007). A nonlinear dynamic model for heart rate response to treadmill walking exercise. IEEE Engineering in Medicine and Biology Society, pages 2988 – 2991. • Mohammad et al. (2011): Mohammad, S., Guerra, T. M., Grobois, J. M., and Hecquet, B. (2011). Heart rate control during cycling exercise using takagi-sugeno models. 18th IFAC World Congress, Milano (Italy), pages 12783 – 12788. • Ludwig et al. (2015): Ludwig, M., Sundaram, A. M., Füller, M., Asteroth, A., and Prassler, E. (2015). On modeling the cardiovascular system and predicting the human heart rate under strain. Proceedings of the 1st International Conference on Information and Communication Technologies for Ageing Well and e-Health (ICT4AgingWell), pages 106 – 117. https://www.h-brs.de/en/s4s 32

Additional slides: The idea behind the four parameters

Convolution Model 𝒃 𝟓 + 𝒃 𝟒 1 𝒃 𝟐 ⋅ 𝑣 ∗𝑓 Τ ∙ 𝒃 𝟐 𝑧 𝑢 = 𝒃 𝟑 ⋅ 𝑢 35

Baseline: neutral parameters 𝑏 1 = 𝑏 2 = 0.01, 𝑏 3 = 0, 𝑏 4 = 1 36

Convolution Model 𝒃 𝟓 + 𝒃 𝟒 1 𝒃 𝟐 ⋅ 𝑣 ∗𝑓 Τ ∙ 𝒃 𝟐 𝑧 𝑢 = 𝒃 𝟑 ⋅ 𝑢 • 𝑏 2 : impact parameter 37

Influence: proportional reaction to strain 𝑏 1 = 0.01, 𝑏 3 = 0, 𝑏 4 = 1 38

Convolution Model 𝒃 𝟓 + 𝒃 𝟒 1 𝒃 𝟐 ⋅ 𝑣 ∗𝑓 Τ ∙ 𝒃 𝟐 𝑧 𝑢 = 𝒃 𝟑 ⋅ 𝑢 • 𝑏 2 : impact parameter • 𝑏 4 : slope parameter 39

Influence: scaling „ extrema “ 𝑏 1 = 0.01, 𝑏 3 = 0 40

Convolution Model 𝒃 𝟓 + 𝒃 𝟒 1 𝒃 𝟐 ⋅ 𝑣 ∗𝑓 Τ ∙ 𝒃 𝟐 𝑧 𝑢 = 𝒃 𝟑 ⋅ 𝑢 • 𝑏 2 : impact parameter • 𝑏 3 : level parameter • 𝑏 4 : slope parameter 41

Influence: resting heart rate 𝑏 1 = 0.01 42

Convolution Model 𝒃 𝟓 + 𝒃 𝟒 1 𝒃 𝟐 ⋅ 𝑣 ∗𝑓 Τ ∙ 𝒃 𝟐 𝑧 𝑢 = 𝒃 𝟑 ⋅ 𝑢 • 𝑏 1 : memory parameter • 𝑏 2 : impact parameter • 𝑏 3 : level parameter • 𝑏 4 : slope parameter 43

Influence: time, duration, former strain 44

Parameter: Exponential vs. Multiplicative Exponential impact Multiplication impact 45

Additional slides: Competitiveness

Competitiveness 47

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