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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

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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 Β· November 2016

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A Convolution Model for Heart Rate Prediction in Physical Exercise

Melanie Ludwig, Harald G. Grohganz, Alexander Asteroth

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3

?

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Wha hat is is he hear art rat ate e mod

  • delling

elling?

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Heart Rate Modelling

Model

Output

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Input Parameter

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Heart Rate Modelling

Model

Parameter Heart rate

Τ¦ 𝑏 𝑣 Optimized with measured heart rates from previous trainings

𝑧 𝑒 ≔ β„³ Τ¦ 𝑏, 𝑣

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Wattage

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Requirement: Heart Rate Prediction

Simulation

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How

  • w to

to us use he heart art rat ate e models

  • dels?
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Usually…

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

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Now…

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

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Heart Rate Prediction Models

  • Usually [e.g.: 1, 2]:
  • Predicting some seconds into the future
  • Used for (automatic) control systems
  • Applicability for complete HR curve prediction?
  • Preceding study: comparement of literature models
  • 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)

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Can Can we we us use he hear art rat ate e models

  • dels

to to pr predict edict a a com

  • mplete

plete he hear art rat ate e cur urve ve?

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Example: LTI Model

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LTI model: Cheng et al. (2007)

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Example: Takagi-Sugeno Model

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TS model: Mohammad et al. (2011)

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Example: Takagi-Sugeno Model

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TS model: Mohammad et al. (2011)

Strongly dependent on the data and the way of parameter fitting οƒ  Overfitting?

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The Convolution Model

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How

  • w can

an we we pr predic edict a a com

  • mplete

plete he hear art rat ate e cur urve ve?

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Convolution Model

𝑧 𝑒 = π’ƒπŸ‘ β‹…

1 π’ƒπŸ β‹… 𝑣 βˆ—π‘“ Ξ€ βˆ™ π’ƒπŸ 𝑒 π’ƒπŸ“ + π’ƒπŸ’

  • 𝑏1: memory parameter
  • 𝑏2: impact parameter
  • 𝑏3: level parameter
  • 𝑏4: slope parameter

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Data

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

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Data

  • 4+5+8 data sets οƒ  30 prediction experiments
  • fitting on at least 2 training sessions

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# data sets Fitting on … Prediction on … # of prediction experiments 4 (subj. #3) <1,2>; <1,2,3> 3,4; 4 ෍

𝑗=1 2

𝑗 = 3 5 (subj. #1) <1,2>; <1,2,3>; <1,2,3,4> 3,4,5; 4,5; 5 ෍

𝑗=1 3

𝑗 = 6 8 (subj. #2) <1,2>; <1,2,3>; …; <1,2,3,4,5,6,7> 3,…,8; 4,…,8; … ; 7,8; 8 ෍

𝑗=1 6

𝑗 = 21

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First Competitiveness

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En Enha hancement ncement: Are e these hese pa parameters ameters sui uitable table for

  • r

mod

  • delling

elling fit itne ness ss?

?

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Parameter Reduction

𝑧 𝑒 = 𝑏2 β‹…

1 𝑏1 β‹… 𝑣 βˆ—π‘“ Ξ€ βˆ™ 𝑏1 𝑒 𝑏4 + 𝑏3

  • 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 𝑏3 to resting heart rate,

fixed exponential parameter 𝑏4 to 0.9, polynomial linkage of parameter 𝑏1 and 𝑏2 (6.31 bpm)

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Reduced Convolution Model

𝑧 𝑒 = 𝜷 β‹…

1 𝑏1 β‹… 𝑣 βˆ—π‘“ Ξ€ βˆ™ 𝑏1 𝑒 0.9

+ HRrest with 𝑏1 = 2.06 + 158.8 β‹… 𝜷 βˆ’ 36750 β‹… 𝜷2

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Parameter Reduction

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Correlation: 𝛽 and fitness?

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Completely untrained before Christmas break in training Form on the day?

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Correlation: 𝛽 and fitness?

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Next ext steps eps?

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Future Work

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

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Future Work

  • Validation of a possible correlation between

𝛽 and the subjectβ€˜s fitness

  • More subjects
  • Evaluation with professional athletes for better benchmark
  • Correlation with Lactate / maxLASS?

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Conclusion

  • Difficult to use existing heart rate models for prediction
  • Often too many parameters (unstable)
  • Convolution Model for predicting a whole heart rate curve
  • Low errors around 6 bpm
  • Huge reduction of complexity:

using only one parameter (might indicate fitness!)

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!?

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References

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  • 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., FΓΌller, 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

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Additional slides: The idea behind the four parameters

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Convolution Model

𝑧 𝑒 = π’ƒπŸ‘ β‹…

1 π’ƒπŸ β‹… 𝑣 βˆ—π‘“ Ξ€ βˆ™ π’ƒπŸ 𝑒 π’ƒπŸ“ + π’ƒπŸ’

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Baseline: neutral parameters

𝑏1 = 𝑏2 = 0.01, 𝑏3 = 0, 𝑏4 = 1

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Convolution Model

𝑧 𝑒 = π’ƒπŸ‘ β‹…

1 π’ƒπŸ β‹… 𝑣 βˆ—π‘“ Ξ€ βˆ™ π’ƒπŸ 𝑒 π’ƒπŸ“ + π’ƒπŸ’

  • 𝑏2: impact parameter

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Influence: proportional reaction to strain

𝑏1 = 0.01, 𝑏3 = 0, 𝑏4 = 1

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Convolution Model

𝑧 𝑒 = π’ƒπŸ‘ β‹…

1 π’ƒπŸ β‹… 𝑣 βˆ—π‘“ Ξ€ βˆ™ π’ƒπŸ 𝑒 π’ƒπŸ“ + π’ƒπŸ’

  • 𝑏2: impact parameter
  • 𝑏4: slope parameter

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Influence: scaling β€žextremaβ€œ

𝑏1 = 0.01, 𝑏3 = 0

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Convolution Model

𝑧 𝑒 = π’ƒπŸ‘ β‹…

1 π’ƒπŸ β‹… 𝑣 βˆ—π‘“ Ξ€ βˆ™ π’ƒπŸ 𝑒 π’ƒπŸ“ + π’ƒπŸ’

  • 𝑏2: impact parameter
  • 𝑏3: level parameter
  • 𝑏4: slope parameter

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Influence: resting heart rate

𝑏1 = 0.01

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Convolution Model

𝑧 𝑒 = π’ƒπŸ‘ β‹…

1 π’ƒπŸ β‹… 𝑣 βˆ—π‘“ Ξ€ βˆ™ π’ƒπŸ 𝑒 π’ƒπŸ“ + π’ƒπŸ’

  • 𝑏1: memory parameter
  • 𝑏2: impact parameter
  • 𝑏3: level parameter
  • 𝑏4: slope parameter

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Influence: time, duration, former strain

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Parameter: Exponential vs. Multiplicative

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Exponential impact Multiplication impact

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Additional slides: Competitiveness

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Competitiveness

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