Anxiety Management: Breathing & Arousal Regulation

Autonomic State

Arousal (sympathetic drive)22%

HRV coherence10%

Heart rate

72 bpm

Catastrophizing

low

Paced Breathing

Inhale…

Breaths per minute 6.0

Anxiety Triggers

How it works

Arousal A (0–1, simulated sympathetic activation) follows a driven relaxation model:

dA/dt = -k(f) · A + S(t) - r · reappraisal
k(f)  = k0 + kmax · exp(-(f-0.1)² / (2σ²))

f is breathing frequency in Hz (bpm/60). The recovery rate k(f) peaks at f ≈ 0.1 Hz — six breaths per minute — because that matches the resonance frequency of the baroreflex loop, the real physiological basis of HRV biofeedback training used in clinical anxiety treatment. Breathing near resonance drains arousal fastest.

Heart rate oscillates with breathing through respiratory sinus arrhythmia (RSA): HR = HR_base + 26·A + G(f)·sin(2πft), where the RSA gain G(f) is also largest at the resonance frequency — this is what produces the smooth, high-amplitude heart-rate wave ("coherence") seen in real biofeedback devices. Coherence here is measured as that oscillation's amplitude relative to arousal-driven noise.

Stressor buttons inject a step into S(t), spiking arousal and adding to a catastrophizing accumulator. Cognitive reappraisal (a core CBT technique — deliberately reframing a threat appraisal) applies an immediate arousal reduction r and decays the catastrophizing accumulator, modelling how reframing a thought interrupts the physiological stress response rather than only the thought itself.

Sympathetic (stress) particles Calm / parasympathetic particles Breath pacer ring

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