Each breath modulates heart rate through the vagus nerve's beat-to-beat braking of the sinoatrial node — this is respiratory sinus arrhythmia (RSA). Heart rate is modelled as a baseline plus a breathing-driven oscillation lagged by the ~0.9 s baroreflex delay:
- HR(t) = 68 + 14·A·sin(2π·f·(t−0.9)) + jitter
- f = breathing rate in Hz, A = resonance amplitude factor (largest near 6 breaths/min ≈ 0.1 Hz, the baroreflex loop's natural frequency)
- Vagal tone scales A directly — higher parasympathetic drive means a bigger, cleaner swing; lower tone flattens it and adds noise.
The top trace scrolls the breathing waveform (chest expansion); the bottom trace scrolls instantaneous heart rate. Watch the HR trace ripple in lock-step with each inhale/exhale, and grow largest near the resonance preset.