Ballistocardiography: Heartbeat Recoil Sensing

Cardiac Drive

Heart rate 72 bpm

Ejection force 20 N

Patient body mass 70 kg

Motion / respiration noise 15%

Sensor Readout

Measured rate

— bpm

True rate

72 bpm

Peak recoil accel.

0.0 mg

Signal quality

—%

How it works

Ballistocardiography (BCG) does not sense electricity or light — it senses recoil. During systole the heart accelerates a slug of blood up the aorta; by Newton's third law, the reaction force pushes the rest of the body the opposite way, exactly as a cannon recoils when it fires a shell:

F_body(t) = − dp_blood/dt = − F_eject(t)

That force couples into the body through soft tissue, modelled here as a driven mass–spring–damper resting on the sensor plate:

m·x″ + c·x′ + k·x = F_body(t)
a(t) = x″(t)   ← what the accelerometer actually reports

Two consequences fall straight out of the equation, and both are visible if you drag the sliders:

Amplitude ∝ 1/m — for the same heartbeat, a heavier patient produces a smaller measured signal (a = F/m), which is exactly why BCG is notoriously hard to calibrate person-to-person.
Underdamped ringing — each beat doesn't spike and vanish, it rings for a few hundred milliseconds at the body's coupling resonance before the next beat arrives, which is what the waveform strip is drawing.

The blue packets riding up the aortic arc are the ejected mass itself; the arrow at the chest is the instantaneous reaction force, scaled and flipped by −1. The beat detector below finds local peaks in a(t) at least 250 ms apart to estimate a measured heart rate — crank up motion noise and watch it lose the true beat, the same failure mode that makes real bed- and wearable-based BCG sensitive to fidgeting and breathing artifact.

Ejected blood mass Reaction force

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Accelerometer trace a(t)