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How the monitors compute their numbers

Recomputing each monitor numeric from its own waveform finds a short, simple algorithm for every one (a median, an exponential average or a time mean over 3–30 s) and a delay of 2–9 s behind the newest data it uses. No value is stamped before its data exist.
Date 2026-10-12
Status current
Methods Delays and averaging windows
Devices Solar8000 monitor, Primus anaesthesia machine, BIS monitor
Variables Solar8000 heart rate, Solar8000 ART and CVP numerics, Solar8000 pulse rate (PLETH_HR), Primus ETCO₂, PIP and RR, ECG lead II (SNUADC), Arterial pressure (SNUADC), Capnogram (Primus), Airway pressure (Primus)

Background

A numeric summarises a window of signal that ended before its stamp. Knowing the window and the delay lets a value be placed against the physiology it describes, and tells a model when the value could first have been known.

Data

Record rates on 1,000 random cases. The algorithm fit on 24 cases with ECG, arterial pressure, CVP and Primus waveforms; PLETH_HR on 231 cases.

Method

Timing model. A value stamped at t is computed at u = t − d − φ from the data in a window ending at u: d is the processing and transmission delay, and φ is where within the device's update phase the computation fell (uniform over one poll for values the monitor recomputes on its own schedule; over one 0.48 s record for Primus values of the last completed breath). Values are uniform over their reporting bin (rounded or truncated). Every delay is measured from the window's end, the anchor; the window's middle is a derived description only.

Fit. Each numeric was fitted against beat-by-beat or breath-by-breath values from its waveform. Candidates: a mean, median or exponential average over N events or T seconds, rate and waveform-mean variants, delays from −3 to 15 s; the best by likelihood per case. A held-value model (refreshing every 4–12 s) was the alternative.

Results

Record rates: Solar8000 every 2.00 s (99% within ±50 ms), BIS every 1.00 s, Primus about every 7.0 s (or 6.3 s; ±0.4 s, not locked to breaths). Solar8000's ETCO₂ and ventilator values change only every 6–8 s: Primus values relayed through the Solar8000. Every Solar8000 ST_II record is written twice at the same stamp.

Numeric Best fit (cases) Delay from window end
HR median R–R over ~6 s, truncated (14/24) 3.6 s
ART systolic median over 3 s, or EWMA ½ 2.1 s
ART mean EWMA ¼ per beat (16/24) 2.3 s
ART diastolic EWMA ½ (20/24) 1.9 s
CVP waveform mean over 4–5 s (16/21) 5.0 s
PLETH_HR median of ~12 beats (134/231) 3.4 s
Primus RR 60 / mean breath interval over 30 s (17/24) 8.5 s
Primus ETCO₂, PEEP the latest breath 1.8–1.9 s
Primus PIP the latest breath 5.2 s
  • No slow updates: the held-value model lost in every case for HR, ART, CVP and PLETH_HR.
  • HR is truncated, not rounded (24/24); RR clearly rounds.
  • No front-stamping: no numeric is stamped before the data it describes.
Parameter Value Status From
Solar8000 HR window about 6 s (best 6–8 s in both delay groups) measured How the monitors compute their numbers

Discussion

Mean against median, or beats against seconds, often differ by only 0.01–0.05 log-likelihood per record, so the algorithm family is less certain than the delay. Pressure numerics sit about 4 mmHg below the analogue waveform in these cases (scale, not timing); over the whole release the median is −1.2 mmHg, varying by about ±6 mmHg between patients (Minutes of hypotension per patient, from the monitor and from the waveform). Delays here are pilot values; Numeric delays are fixed within a case, different between cases measures them in every case.

Observations it supports

Observation Status Summary
Monitor numerics describe the past, never the future established Every monitor numeric describes a window of 3–30 s or more that ended 1–9 s before its stamp. None is stamped before its data exist, so the stamps already respect the availability rule.
Solar8000 ST records are written twice established Every Solar8000 ST_II record is duplicated at the same stamp (0–20 ms apart).
Solar8000 heart rate is truncated, not rounded established The Solar8000 heart rate drops its fraction (floor), in 24 of 24 pilot cases; the respiratory rate rounds.
The Solar8000 relays the Primus's ventilation numbers established Solar8000 ETCO₂, RR_CO2, VENT_PIP and VENT_RR change only every 6–8 s: they are Primus values passed on through the Solar8000's 2 s polling, not measured by the monitor.

Worked examples

Example Side Status Summary
Cuff pressure against the arterial line both draft 12,238 cuff readings against the arterial line at the cuff's own moment, in 2,283 patients: no bias over the cohort at any pressure, but each patient's cuff reads a constant 10 mmHg (SD) above or below their line, and half the arterial readings below 65 mmHg are not below 65 by cuff.
Minutes of hypotension per patient, from the monitor and from the waveform both draft Minutes with MAP below 65 mmHg in 3,476 recordings, from the monitor's numeric and from the arterial waveform's beats: the two routes to one pressure differ by several mmHg per patient, which moves half of all patients' minutes by 5 or more and a fifth of their labels, and the numeric's averaging hides short dips in every patient.

Code

Figures

Four histograms of record interval in 5 ms bins.
Record intervals cluster tightly around each device’s nominal period, within a few milliseconds for Solar8000 and BIS.
Grid of histograms on a log time axis, one per track, grey for record intervals and coloured for change intervals.
Time between records and between value changes for each numeric track in 1,000 random cases: Solar8000 records every 2 s, Primus about every 7 s, BIS every 1 s.
Schematic ECG with an R–R window, brackets and dimension arrows on a time axis relative to the stamp.
How one recorded numeric value relates to its data window: window length T, processing delay d and poll phase φ.
Three panels: delay dot and interquartile range per numeric, the best-fitting algorithms, and repeat fraction against predicted change.
In a 24-case pilot each monitor numeric is best explained by a short median, exponential or latest-breath window, recorded 2–9 s after its data. Held values repeat even when a large change is predicted.