Poincaré Plot Analysis for PPG HRV

The Poincaré plot is constructed by plotting $\mathrm{IBI}_n$ on the x-axis against $\mathrm{IBI}_{n+1}$ on the y-axis for all successive pairs. In normal sinus rhythm, points cluster along the line of identity ($\mathrm{IBI}_n = \mathrm{IBI}_{n+1}$) in an elongated ellipse. $\mathrm{SD1} = \sqrt{0.5 \times \operatorname{var}\left(\mathrm{IBI}_{n+1} - \mathrm{IBI}_n\right)} = \mathrm{RMSSD}/\sqrt{2}$, capturing beat-to-beat variability perpendicular to the identity line. $\mathrm{SD2} = \sqrt{2\,\mathrm{SDNN}^{2} - 0.5\,\mathrm{RMSSD}^{2}}$ captures dispersion along the identity line, reflecting longer-term variability.

The SD1/SD2 ratio provides a unitless sympathovagal balance index analogous to LF/HF but computed directly from the time domain without spectral estimation. SD1/SD2 < 0.3 suggests sympathetic predominance (reduced parasympathetic modulation); SD1/SD2 > 0.6 suggests parasympathetic predominance. The visual pattern of the Poincaré plot provides qualitative diagnostic information: torpedo-shaped plots indicate healthy sinus rhythm, fan-shaped plots suggest atrial fibrillation, and clustered/compressed plots indicate severely reduced HRV.

For PPG applications, Poincaré metrics are robust to moderate IBI detection noise because SD1 and SD2 are computed from variance statistics that average over many beats. The visual Poincaré plot is increasingly used in consumer wearable apps (Kubios, EliteHRV) to communicate HRV status intuitively to non-technical users.