Recurrent Neural Network to Forecast Sprint Performance

Figures & data

Table 1. Glossary of numeric HRV and omegametry parameters.

Name	Abbreviation	Scale	Units	Interpretation
Adaptation reserve ^†	AR	O	Scale (1–7)	Reflects how long cardiac system can express adaptability.
Aerobic index^†	Aerobic	I	N/A	Reflects state of aerobic metabolic pathways.
Anaerobic index^†	Anaerobic	I	N/A	Reflects state of anaerobic metabolic pathways.
Central nervous system readiness ^†	CNS	O	Scale (1–7)	Comprehensive indicator of central nervous system readiness.
Direct current potential^†	DC^‡	C	mV	Present activation of frontal brain system. Reflects wakefulness.
Fatigue index ^†	Fatigue	O	Scale (1–7)	Reflects temporary state of cardiac system.
Heart rate at anaerobic threshold	HR AN	I	bpm	Overall indicator of endurance level.
High frequency	HF*^‡	C	ms^2	Power in high-frequency range. Reflects parasympathetic activity.
High-frequency normalized units	HF nu	C	N/A	High-frequency power in normalized units.
Low frequency^†	LF*	C	ms^2	Power in low-frequency range. Reflects parasympathetic activity.
Low-frequency normalized units	LF nu	C	N/A	Low-frequency power in normalized units.
Low-frequency/high-frequency ratio	LF/HF*	R	N/A	Reflect sympathetic–parasympathetic balance.
Metabolic grade ^†	Metabolic	O	Scale (1–7)	Comprehensive indicator of metabolic system coordination.
Metabolic reactive index ^†	MRI*	C	N/A	Estimate of overall coordination of metabolic systems.
Parasympathetic activity ^†	PNS	C	s	Indicator of current level of parasympathetic nervous system regulation.
Root mean sum of differences of successive intervals	RMSSD*^‡	C	ms	Square root of sum of difference of sequential cardio intervals. Reflects autonomic activity.
Share of aperiodic influences	AI	C	s	Reflects level of random activity that influences heart rhythm.
Standard deviation of aspirate waves	SDAW*	C	N/A	Reflects level of automatization of heart rhythm regulation.
Standard deviation of normal-to-normal intervals	SDNN*	C	ms	Reflects autonomic regulation from full array of cardio intervals.
Standard deviation of successive differences	SDSD*	C	ms	Standard deviation of differences between adjacent intervals.
Stress index ^†	Stress	O	Scale (1–7)	Level of tension in cardiac system.
Sympathetic activity ^†	SNS	C	%	Indicator of current level of sympathetic nervous system regulation.
Tension index ^†	TI*	C	N/A	Reflects level of centralization of heart rhythm regulation.
Total power	TP*^‡	C	ms^2	Variance of all intervals to reflect level of regulatory system.

C = continuous; I = interval; O = ordinal; R = ratio.

*Log-transformation applied to address positive skewness.

^†Denotes proprietary Omegawave parameter.

^‡Variable selected from ordered lasso regularization.

Figure 1. Sample RNN topologies: (a) Elman and (b) Jordan.

Table 2. Pairwise transfer entropy (TE) against race time with permutation p-values.

Candidate feature	TE (bits)	p
RMSSD*	0.37	<0.001
DC*	0.31	<0.001
SDSD*	0.27	0.004
SDNN*	0.26	0.009
SDAW*	0.26	0.012
HF*	0.22	0.028
TP*	0.19	0.034
SNS*	0.19	0.036
LF*	0.17	0.041
TI	0.09	0.089
AI	0.09	0.116
Aerobic	0.07	0.220
HR AN	0.06	0.394
MRI	0.06	0.406
PNS	0.04	0.434
CNS	0.04	0.456
Stress	0.03	0.482
LF nu	0.03	0.488
HF nu	0.03	0.494
LF/HF	0.02	0.530
Metabolic	0.02	0.592
Anaerobic	0.02	0.622
AR	0.02	0.651
Fatigue	0.01	0.870

*Selected feature from permutation significance.

Figure 2. Terminal model accuracies against held-out test data. Solid black line indicates perfect prediction.

Figure 3. ERNN c-ICE and d-ICE plots of ln-RMSSD stratified by time.

Figure 4. ERNN c-ICE and d-ICE plots of DC stratified by time.