Performance modelling and tapering

Iñigo MujikaDepartment of Research and Development

ATHLETIC CLUB BILBAO

Mathematical modelling and systems theory

Athlete = System

Fitness

Fatigue

ΣTraining-

+

Performance

Banister & Fitz-Clarke J. Therm. Biol. 18: 587-597, 1993

Modelling the effects of training

Mujika et al. Med. Sci. Sports Exerc. 28: 251-258, 1996

Time

Training

Performance

Initial

NegativeInfluence

Positive influence

tn tg

Characterisation of a dynamical process

Busso & Thomas Int. J. Sports Physiol. Perf. 1: 400-405, 2006

?

tt

Input OuputSystem

. . . . .

Goodness-of-fit

Weeks of Training

90

92

94

96

98

100

102

0

1

2

3

4

PINI

020406080

100120

45403530252015105085

90

95

100

105

Modeled PerformanceActual Performance

454035302520151050

454035302520151050

Performance (% PB)

Positive Influence (PI) Negative Influence (NI)

Training Load (A.U. wk-1).

Mujika et al. Med. Sci. Sports Exerc. 28: 251-258, 1996

Modelling application in swimming

Mathematical modelling and taper duration

Mujika et al. Med. Sci. Sports Exerc. 28: 251-258, 1996

Time

Training

Performance

tg = 32 ± 12 days

tn = 12 ± 6 days

tn tg

Mujika et al. Med. Sci. Sports Exerc. 28: 251-258, 1996

T39293949596979899

100

Positive Influence (PI)

Early Season Pre-Taper Post-Taper

T1 T2ES0,51,01,52,02,53,03,5

***

Negative Influence (NI)

T1 T2 T3ES

Modelling the effects of the taper

Varying adaptation profiles

Time

Training

10

Performance

24

Swimmer HR

14 38

Swimmer CJ

Limitations and model evolution

“The theoretical analysis based on the original model of Banister et al. (1975) is possibly flawed because of the underlying linear formulation. The response to a given training dose was independent of the accumulated fatigue with past training. This implies that the taper duration should be identical whatever the severity of the training preceding the taper ”

“This led us to propose a formulation of a new non-linear model. This non-linear model implied that the magnitude and duration of the fatigue produced by a given training dose increased with the repetition of exercise bouts, and was reversed when training was reduced (Busso, 2003)”

Thomas et al. J. Sports Sci. 26: 643-652, 2008

Prediction of system’s behaviour from previous observation

Busso & Thomas Int. J. Sports Physiol. Perf. 1: 400-405, 2006

Model&

Parameters?

tt

Input Ouput

Model&

Parameters?

tt

Input Ouput

Characteristics of the optimal simulated taper

% Reduction

Form of training reduction

Step Exponential

65.3

67.4

54.7*$

51.6*$

Without OT

With OT

Linear

46.3*

43.1*

Duration(days)

16.4

22.4

22.3*

39.1*

Without OT

With OT

25.4*

42.5*

Performance(% Personal record)

101.1

101.4

101.1

101.5*

Without OT

With OT

101.1

101.5*

*: different from Step; $: different from Linear

Thomas et al. J. Sports Sci. 26: 643-652, 2008

Effects of previous training on optimal taper characteristics

Without OT With OT0

1

2

3

4

5

6 *

Optimal Training Load(Training Units)

Without OT With OT0

20

40

60

80

100

Optimal Reduction(% Pre-Taper Training)

Without OT With OT0

5

10

15

20

25

30 *

Optimal Duration(Days)

Without OT With OT0

1

2

3

4

5 **

Performance Improvement(% Pre-Taper Performance)

Thomas et al. J. Sports Sci. 26: 643-652, 2008

Effects of optimal taper on NI, PI and performance

Pre Post0

1

2

3

4

5

*

Negative Influence

Pre Post97

98

99

100

101

102

Positive Influence

Pre Post97

98

99

100

101

102 *

Performance(% Personal Record)

WITHOUT OT

Pre Post0

1

2

3

4

5

*

Negative Influence

Pre Post97

98

99

100

101

102

Positive Influence

Pre Post97

98

99

100

101

102

Performance(% Personal Record)

WITH OT

$

* $

*

$

$

Thomas et al. J. Sports Sci. 26: 643-652, 2008

Changes in training load during optimal two-phase taper

0

20

40

60

80

100

120

Weeks of Taper

Training Load (%NT)

0 1 2 3 4 5 6

Thomas et al. J. Strength Cond. Res. Submitted

* $

NT

OT

Performance changes during optimal two-phase taper

96

97

98

99

100

101

102

Weeks of Taper

Performance (%NT)

0 1 2 3 4

103

104

NT

OT2726 28 29 30

103,40

103,45

103,50

103,55

Days of Taper

Performance

Optimal linear taper

Optimal two-phase taper

Thomas et al. J. Strength Cond. Res. Submitted

Conclusions

Conclusions

The available data on performance modelling confirm the relevance of the modelling approach in the study of individual responses to training and the optimisation of tapering strategies

Computer simulations based on mathematical modelling offer new prospects for further investigation into innovative tapering strategies and performance optimisation

ESKERRIK ASKO!(“Thank you very much!” in Basque Language)