The stamp sawtooth model for SNUADC and BIS¶

Fitting each track's record stamps against its sample count as a drift with corrections (a sawtooth) puts SNUADC and BIS on one timeline without any artefact. Checked against shared bursts, the EEG–ECG timing error falls from about 790 ms on the recorded stamps to 33 ms with one constant per SNUADC mode in the pilot, and 42 ms over the whole release.


Date	2026-10-12
Status	current
Methods	Reading the stamps, One event, two clocks
Techniques	Sawtooth fit, Windowed cross-correlation
Clocks	SNUADC sample clock, BIS clock, Recorder PC clock
Devices	SNUADC, BIS monitor, Vital Recorder
Variables	ECG lead II (SNUADC), BIS EEG

Background¶

Between corrections a device stamps by its own sample count, so the offset between two devices ramps at the difference of their clock rates; the corrections pull each device back towards the recorder's clock. Both are visible in the stamps alone (Shared bursts between the ECG and the EEG).

Data¶

191 benchmark cases with BIS; validation on 143 cases with at least 5 good burst windows each way, and on 3,683 ten-minute windows in 165 cases. Later refitted on 250 cases with the signal lost at each SNUADC reset. Rerun on the whole release (19 October): all 5,520 recordings with ECG II and BIS EEG; with the adopted model (model3), 36,928 good burst windows in the 2,710 recordings with at least 5.

Method¶

physiosync's stamp_clock takes each record's stamp minus the time given by the sample count. It estimates one rate per recording from whole teeth (the drift each correction removes, divided by the time since the last), then one offset per stretch between real gaps; corrected_times places every sample on that line. VitalDB rules: SNUADC corrects downwards and BIS upwards, and steps the other way are gaps; a SNUADC track in frequent-correction mode keeps its stamps; a step-mode track without a whole tooth takes its port's typical rate (−47 to −74 ppm); a BIS track without one takes its unit's mean rate. Since 17 October the 17.7 ms lost at each SNUADC step-mode correction is added back (Paced ECG as an independent clock).

Bar chart of median and 90th-percentile timing error for five correction levels, falling from 792 and 1,005 ms for recorded stamps to 16 and 67 ms for the stamp model with a per-case constant. — *Placeholder figure.* EEG–ECG timing error per 10-minute window at each level of correction (3,683 windows, 165 cases).

Results¶

Whole teeth on 151 SNUADC and 184 BIS tracks of 191; the rates agree with the correction scan where that is plausible.
Within-case SD of the EEG–ECG offset: 137 ms on the recorded stamps, 25 ms on the model (median); the bursts' own noise floor is about 11 ms. Ramps flatten (median slope 53 → 12 ms/h) and lag jumps fall from 1.5 to 0.38 per case.
A constant offset is left: EEG minus ECG −803 ms in step mode (117 cases) and −690 ms in frequent-correction mode (29 cases), tight within a port or unit.

Correction	Median error	p90
Recorded stamps	792 ms	1,005 ms
Stamps minus one constant	126 ms	259 ms
Model minus one constant	38 ms	154 ms
Model minus the SNUADC mode's constant (leave-one-out; no artefact needed)	33 ms	116 ms
Model minus the case's own constant from its bursts	16 ms	67 ms
Whole release (19 October). The model's ECG–EEG burst check, rerun on every recording
(`tools/burst_validation_agg.py`):

The constants hold: EEG minus ECG −804.5 ms in step mode (1,530 recordings; interquartile range −835 to −776) and −667.5 ms in frequent-correction mode (78), against −803 and −690 ms on the benchmark.
Where both clocks have whole teeth (377 recordings) the result matches the benchmark: within-recording SD 18 ms, drift left 8.7 ms/h (median absolute slope). Against the step-mode constant, a typical window is off by 35 ms (median; p90 135 ms).
Recordings with no SNUADC correction at all (1,099) were the weak spot. The first model read them as frequent-correction mode and gave the SNUADC no drift, but their EEG–ECG offset drifted by a median of −176 ms/h, the step-mode drift: these are step-mode recordings that end before the first reset.
Giving them their port's step-mode rate fixes most of it (model2, rerun on every recording, tools/sa_corrected.py). For these 1,096 recordings:

	Drift assumed 0	Port's step-mode rate
Within-recording SD (median)	62 ms	25 ms
Drift left (median slope)	−176 ms/h	−11 ms/h
Drift left (median absolute slope)	183 ms/h	74 ms/h
Error against the mode's constant (median; p90)	81; 208 ms	63; 177 ms

What is left is spread both ways (p10–p90 −135 to +122 ms/h): each recording's SNUADC drifts at its own rate, not its port's median. - The same for the BIS (model3). A BIS that makes no correction also got zero drift. Giving it its port's median BIS rate against the recorder PC (+16 to +50 ppm by port, from the correction steps of the full release, never from the bursts) fixes the 236 recordings where that happens:

BIS with no correction	Recordings	Drift left (median), model2 → model3	Within-recording SD
Shorter than the 8,192 s BIS timer	202	−92 → −16 ms/h	21 → 17 ms
Longer	34	−66 → −14 ms/h	32 → 28 ms

Over all recordings the gain is small (within-recording SD 23.9 → 23.4 ms; median absolute slope 42.6 → 40.3 ms/h), because few recordings are affected. - Over all 2,707 recordings with model2: a median error of 42 ms against the mode's constant and 18 ms against the recording's own constant (p90 151 and 79 ms); within-recording SD 24 ms (first model: 46, 22, 165, 106 and 34 ms). - The adopted model (model3), over all 2,710 recordings with at least 5 good windows: EEG minus ECG −804 ms in step mode (1,526 recordings; interquartile range −833 to −776), −660 ms in frequent-correction mode (78), and −766 ms with no SNUADC correction (1,099). A median error of 42 ms against the mode's constant (p90 150 ms) and 17 ms against the recording's own constant (p90 79 ms); within-recording SD 23 ms. These are the values in EEG–ECG constant after the stamp model and EEG–ECG timing error after the stamp model. (The first bullet above is the first model, before the recordings with no correction were given a rate.)

Three panels; a sharp peak near −805 ms for step mode; two cumulative curves rising between 10 and 200 ms; a slope histogram with a narrow blue peak at zero and wider orange and grey humps also centred at zero. — The stamp model checked with ECG–EEG bursts in every recording (19 October). Left: the constant left after the model, per recording, by SNUADC correction mode. Middle: the remaining timing error per 10-minute window, against the mode's constant (leave-one-out) and the recording's own. Right: the drift left over each recording: near zero where both clocks were fitted from whole teeth (blue), and centred near zero, but wider, where the SNUADC made no correction and was given its port's step-mode rate (grey; model3, which also gives a BIS with no correction its port's rate). Before that change the grey group sat near −176 ms/h.

What this looks like in one recording, together with the Primus:

Six panels over 9 hours. Left column: sawtooth lines for SNUADC and BIS and a rising line for the Primus spanning about 3.5 seconds; burst lags ramping between minus 0.6 and minus 1.2 seconds; breath lags rising from minus 2 to plus 2 seconds. Right column: the same quantities flat near zero. — One recording (case 1216, 8.7 hours), before synchronisation (left) and after (right), on the same scales. Top: each clock's time minus the synchronised time. The SNUADC's stamps drift and are pulled back by half a second about every two hours; the BIS's stamps sit about 0.8 s off and are pushed forward every 8,192 s; the Primus drifts about 4 s over the recording and steps at its airway-pressure pauses (dotted lines). After synchronisation the typical error left is about 3 ms (SNUADC), 42 ms (BIS) and 55 ms (Primus, whole-release medians; bands). Middle: the same electrocautery and muscle bursts seen in the ECG and the EEG, as recorded and on the synchronised times, a check independent of the correction. Bottom: the airway-to-central-venous pressure lag of the breath cycle, as recorded and, after, as the error left when each 10-minute window is predicted from all the others.

Parameter	Value	Status	From
BIS drift against the recorder PC	25 ppm (p10–p90 12 to 50; 5th–95th 7.3–51.1 ppm; census fit of 4,728 recordings median 21.1 ppm)	measured	The stamp sawtooth model for SNUADC and BIS
SNUADC step-mode drift	−63 ppm (p10–p90 −79 to −44; 5th–95th −80.3 to −36.9 ppm; medians of −46 to −74 ppm by serial port)	measured	The stamp sawtooth model for SNUADC and BIS
EEG–ECG constant after the stamp model	−804 ms in step mode (1,526 recordings); −660 ms in frequent-correction mode (78)	measured	The stamp sawtooth model for SNUADC and BIS
SNUADC step-mode correction interval	2.08 h (5th–95th 1.65–3.57 h between resets; per-recording means p10–p90 1.68–3.07 h)	measured	The stamp sawtooth model for SNUADC and BIS
EEG–ECG timing error after the stamp model	42 ms median, p90 150 ms (17 ms and 79 ms with the recording's own bursts)	measured	The stamp sawtooth model for SNUADC and BIS

Discussion¶

The model needs no artefact; the bursts only check it and supply the constant. With the constant for the case's SNUADC mode, a typical window lines up to about 42 ms over the whole release (33 ms in the pilot); with the recording's own bursts, to about 17 ms. These are the numbers behind the BIS EEG "after sync" timing in the planner.

Observations it supports¶

Observation	Status	Summary
About 20 ms of signal lost at every SNUADC reset	established	At each step-mode reset the acquisition pauses for about 20 ms inside the last record before the new timing, and that time is never sampled: 17.7 ms on the sample count (Signal lost at a SNUADC step-mode correction), once the filler sample is counted. Every record still holds 100 samples, so nothing in the file shows it.
SNUADC sends no time; the recorder stamps by count	established	The SNUADC board streams samples with no time stamps. Every SNUADC time in VitalDB is the recorder's model of the board's clock: the sample count at the nominal rate, pulled back when it drifts too far.
The EEG–ECG offset is fixed by the SNUADC correction mode	established	After the stamp model, BIS EEG still lags the SNUADC ECG by a constant: −804 ms in step mode and −660 ms in frequent-correction mode over the whole release, tight within a port or unit. The mode, a property of the setup, sets the constant.

Limitations¶

Recordings that change correction mode partway, or have many gaps, still fail (p99 about 250 ms). The error distributions come from the bursts, so they include the probe's own noise.

Open questions¶

Recordings without a SNUADC correction (next step). Giving the 1,096 recordings without a SNUADC correction their port's step-mode rate removed most of their drift (median −176 to −11 ms/h), but each still drifts at its own rate (p10–p90 −135 to +122 ms/h left). A per-recording rate cannot come from the stamps: with no correction they carry no information about the recorder PC (the census gives −1.0 ppm, the stamp arithmetic, for all of them). It needs a clock tied to the PC that shares events with the SNUADC (bursts against a BIS with whole teeth, in 122 recordings; calibration, so tested on held-out windows), or the setup's unit. Where the BIS has teeth the bursts imply the SNUADC drifts about −36 ppm rather than −63, the fast-BIS, slow-SNUADC pattern of When each device's clock is corrected, in every recording's open question.
Recordings that change correction mode partway (unexplained phenomenon). Recordings that change correction mode partway still fail the model (p99 about 250 ms). Why a recording changes mode, and how to fit both parts, is open.
Why the constant offset differs between modes (unexplained phenomenon). The EEG lags the ECG by −0.80 s in step mode and −0.66 s in frequent mode after the model (whole release; −0.69 s in the pilot); why the constant differs between modes is not known.

Worked examples¶

Example	Side	Status	Summary
Pulse pressure variation gated by ventilator breaths	time	draft	Pulse pressure variation per ventilator breath, in 3,448 recordings: the ventilator's clock sits a median 1.8 s off the arterial line's, which moves half of all breaths' values by a point or more and scatters where in the breath the pulse pressure peaks; a recording's median PPV hardly changes.

Code¶

Figures¶

Six scatter plots of recorded against model stamps beside bars of error by correction level and two histograms. — The stamp sawtooth model flattens the EEG-minus-ECG offset in case 4644, case 2580, case 750 and case 1703 (step mode) and in case 359 and case 5780 (small-correction mode). With a per-case constant the median timing error falls from 792 ms to 16 ms.