The PPG sawtooth and its correction¶

The ECG→PPG delay creeps at 18–52 ppm and jumps up by one 33.3 ms frame at each slip, every 11–31 minutes. A tooth-by-tooth model removes it; where the correction is confident it is essentially exact on injected test data.


Date	2026-10-10
Status	current
Methods	Clocks carried in the signal
Techniques	Beat matching, Phase-step detection, Null controls
Clocks	Pulse oximeter frame clock, SNUADC sample clock
Devices	SNUADC, Solar8000 monitor
Variables	Plethysmogram (SNUADC), ECG lead II (SNUADC)

Background¶

SNUADC samples ECG and PPG together, so its own drift cannot move one against the other. Any drift between them comes from inside the monitor.

Data¶

The same 266 cases (378 hours); a benchmark of a known sawtooth injected into 35 real recordings without one.

Method¶

The PPG delay is modelled as D(t) = offset + frame × (slips so far) − creep. The fit detects resets in the beat-matched pulse arrival time and keeps a slip only if it is one frame and falls between two beats (physiological changes build over several beats); puts back missed slips only where a gap holds whole teeth and the data show a step; gives each tooth the creep rate frame ÷ length, so a wrong slip distorts only its own tooth; and shifts the median to the adopted pulse arrival time. Each tooth gets a confidence tier: A (rate corroborated, clean slips, low noise), B, C, N (no sawtooth evident for 45 minutes or 1.5 teeth) or U (possibly affected, not corrected).

Results¶

One frame per slip: the step has a median of 32.3 ms (IQR 30.4–34.8); other sizes are no more common than in a sign-flipped control.
Regular: slips recur every frame ÷ rate, stable to about 0.2 ppm; a few recordings creep by about 1 ppm over 90 minutes.
Fixed per setup, 18–52 ppm, unrelated to the SNUADC drift (r = −0.22) or the frame clock (r = 0.13). One port hosts two PPG sources: step-mode cases at 51 ppm and frequent-mode cases at 27 ppm.
Invisible in the waveform: no repeated or held 33 ms segment at a slip (3.5% against 5% by chance).

Tier	Share of injected time	Error after correction (RMS)	Time over 10 ms	Share of real time
A	60%	0.2 ms	0.1%	17.0%
B	17%	1.6 ms	3.7%	12.2%
C	19%	5.3 ms	14%	25.0%
U (not corrected)	3%	9.0 ms	34%	22.8%
N (no sawtooth)	0.5% (wrongly)	—	—	23.0%

Uncorrected, the injected sawtooth has an RMS of 9.5 ms.

Parameter	Value	Status	From
PPG sawtooth rate	18–52 ppm by setup	measured	The PPG sawtooth and its correction
PPG slip size	32.3 ms (IQR 30.4 to 34.8)	measured	The PPG sawtooth and its correction

Discussion¶

Tiers A and B cover 29% of the real time analysed, 52% with the stretches where no sawtooth is running. The benchmark is optimistic: its physiology came from quiet recordings. Labels carry each tooth's tier, so a user can choose how much time to trust.

The last step of the fit, shifting each recording's median to the adopted pulse arrival time, also removes real differences between patients. One device delay for the PLETH across the release later showed that one global delay (385 ms, PPG hardware delay) fits the whole release, so the atlas removes that instead and keeps those differences (Pulse arrival time in two correction steps).

Observations it supports¶

Observation	Status	Summary
The ECG→PPG delay is a sawtooth	established	Inside the oximeter the PPG content creeps 18–52 ppm against its 30 Hz frames; every 11–31 minutes a frame repeats and the delay jumps up by 33 ms. The rate is fixed per recording setup.
The PLETH arrives about 0.4 s late	established	Raw R-to-PPG-foot pulse arrival time in VitalDB has a median of 0.64–0.71 s, about 0.4 s more than physiology: the monitor's buffering and filtering. One delay fits the whole release: no clusters by setup, SNUADC port or case order (One device delay for the PLETH across the release).
The plethysmogram is built in 30 Hz frames	established	The SNUADC PLETH waveform comes from the oximeter in 33.3 ms frames, smoothed to 500 Hz. Its content changes once per frame, on the oximeter's own clock, about 0.4 s after the finger.

Worked examples¶

Example	Side	Status	Summary
Pulse arrival time against blood pressure, before and after synchronisation	time	draft	In 3,270 recordings, PAT tracks systolic pressure only once each pulse is paired with its own beat: the hourly correlation moves from a mean of −0.04 to −0.21 (88% of recordings negative), reproducing Ruffolo et al. 2025 in a second dataset; paired naively, PAT is a heart-rate signal.
Pulse arrival time in two correction steps	time	draft	The time from the ECG R wave to the pulse at the finger, as stored, after the PLETH's sawtooth is removed, and after its device offset is removed, smoothed by maximum likelihood, with the arterial line as the reference.

Code¶

Figures¶

Three long PAT traces of measured and corrected values beside six aggregate histograms and scatter plots. — The sawtooth correction removes the PPG frame slips in case 2156, case 6241 and case 1094 (panels a–c). Across 266 cases the steps shrink from 32 ms to 0.2 ms, and the sawtooth rate groups by recording setup rather than by SNUADC drift (panels d–i).

Twelve scatter plots of 30 s median PAT against hours, with orange dashed vertical lines. — Pulse-foot PAT through 12 cases, SNUADC clock corrections dashed. Most (case 2, case 4194, case 5581) show a regular sawtooth that does not follow the corrections; case 489 shows none; case 3964 and case 1759 are noisy edge cases.