sd2

Poincare Plot Long-Term Variability

Definition

Poincare plot long-term variability. Formally: std((IBI[1:end-1] + IBI[2:end]) / sqrt(2)).

What does normal look like?

Fitted normative prior: Gamma(α = 3.731, θ = 18.73), KS p = 1.8e-24, n = 61715.

Empirical distribution over the pooled nsrdb+nsr2db normative windows (360-beat windows, 120-beat stride), overlaid with the fitted Gamma prior density. Vertical lines mark the median and the 5–95% range.

Normal-range summary (pooled nsrdb+nsr2db)

n varies by feature only through per-window validity over the full pooled nsrdb+nsr2db table (n up to 61 715; e.g. sampen/mse drop windows where the statistic is undefined). ulf is the one exception: a 360-beat (~5 min) window contains no ULF-band power, so it uses a long-window NSRDB-only extraction (see its own page).

Use cases

• Long-term Poincaré-plot length; overall/continuous variability.
• Paired with SD1 for the SD2/SD1 shape ratio.
• Geometric complement to SDNN.

Applications by area

Evidence is reported at the measure-family level; a specific variant may not be the exact index measured in every cited study.

Clinical

Coverage: statistics. A pooled literature; reviews or meta-analyses exist.

A well-established clinical output across cardiology, endocrinology and psychiatry: lower SD1/SD2 (reduced beat-to-beat and long-term variability) consistently marks worse disease state, though most reported sample sizes are small (n = 18–95). SD1 is mathematically identical to RMSSD (SD1 = RMSSD/√2), so papers reporting both as independently "significant" double-count the same statistic, and the SD2/SD1 ratio's billing as a "sympathovagal balance" surrogate is directly contested.

Dominant reported direction: down: lower SD1/SD2 → worse disease state.

Key references: (Ciccone et al., 2017); (Rahman et al., 2018); (Stuckey et al., 2014).

Sports & peak performance

Coverage: individual papers. A small, scattered literature with no pooled meta-analysis.

Largely restates RMSSD-based vagal-tone monitoring in geometric form (SD1 = RMSSD/√2), plus an SD2/SD1 "stress score" aimed at overreaching detection; SD1 rises with aerobic training and falls with acute intensity/overtraining, though overtraining shows a non-monotonic pattern (higher than sedentary, far below trained) and no meta-analysis isolates a Poincaré-specific effect size distinct from RMSSD.

Dominant reported direction: up with training, down acutely/with overtraining (same underlying signal as RMSSD).

Key references: (Bellenger et al., 2016); (Ciccone et al., 2017).

Contemplative practice

Coverage: individual papers. A small, scattered literature with no pooled meta-analysis.

A handful of small, likely underpowered studies (n = 8–18) report SD1/SD2-ratio changes across meditation traditions, but the direction of SD2 and total Poincaré-plot area disagrees between the two studies that report it: exploratory, not established.

Dominant reported direction: inconsistent across the two available small studies.

Key references: (Ciccone et al., 2017).

See the effect-distribution meta-analysis page for the harvested per-study effect sizes/p-values behind these domain summaries (docs/zoo_gen/effect_stats.csv).

Resources

Resource-intensity rank ◍◍◌◌◌ low is measured: median wall-clock time and allocations over a 360-beat window on synthetic realistic RR (docs/zoo_gen/bench_resources.jl; full grid in resource_bench.csv).

Cold = fresh memoization caches (builds every shared representation from scratch); warm = shared representations (diff, periodogram, Poincaré coords, DFA fluctuation) already cached, so only this feature is recomputed. The tier is derived from the cold cost; see Geometric subgraph (Poincaré coords / RR histogram + reductions). Warm (shared representation cached) is 5× cheaper.

Citation

Tulppo et al. (1996) introduced ellipse-fitted SD2; Brennan et al. (2001) derived the closed form linking it to SDNN/SDSD (primacy contested).

Seminal reference(s): (Tulppo et al., 1996); (Brennan et al., 2001).

See the References page for the full bibliography.