1. Pick an Activity
2. Watch the Heart
The heart squeezes on every R wave. The blue circle is the chest filling and emptying with each breath. When you change activity, the heart rate takes a few seconds to catch up, just like a real horse.
3. The ECG
One line of the electrocardiogram, scrolling like the paper strip at the vet. Each small square is 0.04 s. P = the atria fire, QRS = the ventricles fire (the big spike), T = the ventricles recharge. In Duque's strap lead the T wave points down.
4. The Rhythm
Each dot is one heartbeat: the time since the previous beat (the RR interval). A perfect metronome would be a flat line. Breathing makes the dots rise and fall (faint blue curve); the random wander x in card 5 adds drift and scatter. SDNN and RMSSD are the two numbers vets and researchers use for heart-rate variability (HRV).
5. The Math Behind It
dθ/dt = ω(t) = 2π · HR(t) / 60
ECG(θ) = Σᵢ aᵢ · exp( −(θ − θᵢ)² / 2bᵢ² ) + baseline
One clock hand (θ) sweeps around once per heartbeat. Each wave is a bump of height aᵢ and width bᵢ sitting at its own angle θᵢ on the clock face: P, Q, R, S, T. The ECG is just the sum of the bumps as the hand passes them. (Model: McSharry, Clifford, Tarassenko & Smith, 2003.)
HR(t) = HR₀ · (1 + RSA · sin 2πφbreath) · (1 + x)
dx = −(x / τ) dt + σ dW
The heart rate is a set point HR₀, swayed by breathing, times a wandering factor x that follows a stochastic differential equation. The first term is a spring: it pulls x back toward 0 with memory time τ. The second term is random kicks from the nervous system (a Wiener process, dW). Switch the kicks off and the spring wins: the wander dies away. This is an Ornstein–Uhlenbeck process, the simplest SDE there is. The wander-size slider sets the long-run standard deviation s of x, so σ = s·√(2/τ).
Short τ with kicks on: beat-to-beat scatter (RMSSD climbs). Long τ: slow drift that lasts many beats (SDNN climbs, RMSSD barely moves). Kicks off: watch the wander decay with time τ, then only the breathing sway remains.
A dropped beat: the atria fire (P wave) but the signal never reaches the ventricles, so no QRS and no T. Fit horses often do this a few times a minute while standing quietly. It should vanish when they move.
Turn rate adaptation off and push the heart rate past 150: the T wave of one beat runs into the P wave of the next. Real hearts avoid this because the ventricles recharge faster at high rates (the QT interval scales with the square root of the RR interval, Bazett's rule).
6. Real Horse Data
| Duque (strap) | Your model | |
|---|---|---|
| Heart rate (beats/min) | — | — |
| Mean RR (ms) | — | — |
| SDNN (ms) | — | — |
| RMSSD (ms) | — | — |
Duque wore a Polar Equine strap: one ECG lead at 125 samples per second, plus the strap's own beat detector (red ticks). The strap sometimes misses a beat and reports one interval twice as long. Look for it. The heart did not skip; the strap did. Strap intervals longer than 1.6× the typical beat are left out of the numbers in the table.