VOX analysis specification.

This document describes the implemented browser-side process for R-R artifact correction, DFA Alpha 1 threshold detection, advanced VO2max estimation, and autonomic recovery analysis.

Pre-Processing & Artifact Correction

Raw R-R intervals recorded during maximal exertion are highly susceptible to ectopic beats and signal noise. To calculate fractal scaling exponents (DFA $α_{1}$ ) accurately, artifacts must be corrected without disrupting the time-series integrity.

1. Global Plausibility Cutoff

All intervals falling outside physiological absolutes are flagged as artifacts:

R R_{i} < 250 ms \lor R R_{i} > 2000 ms

2. Adaptive Windowed Median Filtering

To account for the rapid chronotropic trend during a ramp test, a localized moving window ( $N = 11$ ) is applied. The local median $M_{i}$ is calculated for each interval:

M_{i} = median (R R_{i - 5}, \dots, R R_{i + 5})

An interval is flagged if its absolute deviation exceeds a dynamic 20% physiological threshold:

∣ R R_{i} - M_{i} ∣ > 0.2 \cdot M_{i}

3. Cubic Spline Interpolation

Flagged artifacts are not deleted, as doing so would shift the frequency spectrum and destroy fractal continuity. Instead, valid $R R$ points are used to fit a 3rd-degree polynomial cubic spline. The artifact indices are overwritten with these interpolated values, yielding a continuous, sanitized time series rr_clean.

Metabolic Thresholds via Non-Linear HRV

The engine utilizes Detrended Fluctuation Analysis (DFA) to measure the fractal correlation properties of the rr_clean time series. As metabolic stress and hydrogen ion ( $H^{+}$ ) accumulation increase, parasympathetic withdrawal forces the sinoatrial node from a complex fractal state to a rigid, uncorrelated state.

1. Short-Term Scaling Exponent

The RR time series is integrated, divided into local windows, and linearly detrended. The root-mean-square fluctuation $F (n)$ is calculated across window sizes $4 \leq n \leq 64$ . The scaling exponent $α_{1}$ is derived from the slope of the log-log plot:

F (n) \propto n^{α_{1}}

2. Threshold Identification

The pipeline computes DFA $α_{1}$ dynamically over moving time windows to identify precise physiological phase transitions.

Aerobic Threshold (VT1): the exact interpolated timestamp and running speed where $α_{1}$ drops below $0.75$ .
Anaerobic Threshold (VT2): the timestamp where $α_{1}$ reaches $0.50$ .

Advanced VO2max Modeling

Standard metabolic equations assume steady-state conditions, which systematically overestimate oxygen consumption in progressive ramp protocols. VOX uses a multi-variable fusion model to correct mechanical estimations using autonomic efficiency metrics.

1. Mechanical Baseline (ACSM)

Oxygen consumption is calculated based on peak speed $v$ in m/min and fractional incline $g$ :

V O 2_{A C S M} = 3.5 + (0.2 \cdot v) + (0.9 \cdot v \cdot g)

2. Ramp Protocol Calibration (Foster Correction)

The Foster equation corrects the steady-state overestimation inherent in the ACSM model during maximal ramp testing:

V O 2_{F os t er} = (0.869 \cdot V O 2_{A C S M}) - 0.07

3. Aerodynamic Penalty

If the treadmill test was performed at $0%$ incline, a 2% penalty is applied at speeds $> 10 km/h$ to account for the lack of outdoor wind resistance:

V O 2_{M ec h} = V O 2_{F os t er} \cdot 0.98

4. The Metabolic Economy Modifier

Running economy is quantified by analyzing how deep into the mechanical protocol the athlete remained in an aerobic state. Instead of comparing raw speeds, the engine compares the full ACSM metabolic cost at VT1 against the ACSM metabolic cost at peak load, including both speed and incline:

V O 2_{A C S M, V T 1} = 3.5 + (0.2 \cdot v_{V T 1}) + (0.9 \cdot v_{V T 1} \cdot g_{V T 1})

E R = \frac{V O 2 _{A C S M, V T 1}}{V O 2 _{A C S M, P e ak}}

Assuming a baseline $E R$ of $0.70$ , an economy modifier adjusts oxygen demand:

E co n o m y_M o d i f i er = 1.0 - ((E R - 0.70) \cdot 0.25)

V O 2_{A d j u s t e d_M ec h} = V O 2_{M ec h} \cdot E co n o m y_M o d i f i er

5. Physiological Cross-Validation & Final Fusion

The mechanically derived VO2max is cross-validated against the Uth-Sørensen HR-ratio:

V O 2_{P h y s} = 15.3 \cdot (\frac{H R _{ma x}}{H R _{r es t}})

The final reported VO2max uses an 80/20 weighted fusion:

V O 2_{F ina l} = (0.80 \cdot V O 2_{A d j u s t e d_M ec h}) + (0.20 \cdot V O 2_{P h y s})

Autonomic Recovery Dynamics

Post-exertion data is isolated to evaluate capacity for lactate clearance and parasympathetic reactivation.

1. Heart Rate Recovery

Heart rate recovery is measured at exactly 60 and 120 seconds post-termination ( $T_{0}$ ):

H R R_{60} = H R_{ma x} - H R_{T_{0} + 60 s}

2. Recovery DFA Alpha 1

The scaling exponent is recalculated exclusively for the $T_{0}$ to $T_{0} + 120 s$ window. A persistent value near $0.50$ indicates severe cellular acidosis blocking vagal tone, while a rapid return toward $1.0$ indicates superior metabolic clearance mechanisms.