BMI = weight / height². BSA uses the formula chosen under Formulas (default Mosteller = √(height[cm] × weight[kg] / 3600)).
Adult BMI categories are shown only for ages 20 and over. Younger people need age- and sex-specific growth references.
Age, sex, height, weight and diabetes status are the same values as Controls → Patient profile; changing them here or there sets the scenario to Custom.
Weight sets the glucose model's distribution volumes and diabetes status selects its parameter set. The label and the weight history stay in this tab.
Use the profile (each switch is kept in this browser):
Bedside calculators turn height, sex, weight and age into the numbers used at the bedside: predicted body weight (ARDS Network formula) and the low tidal volume of 6 mL/kg PBW [72, 73];
the at-least-30 mL/kg crystalloid volume suggested for sepsis-induced hypoperfusion within 3 h (weak recommendation, low-quality evidence) [73];
the 0.5 mL/kg/h urine output below which, for 6 h, KDIGO stage 1 acute kidney injury is met [74]; and the age-predicted maximal heart rate, 208 − 0.7 × age [75].
Shock index (SI = HR / systolic pressure) uses the displayed HR and the last NIBP systolic; the healthy adult range is 0.5–0.7 [76], and SI alone discriminates poorly (AUC 0.58 in that study).
Age × SI is not shown: it was studied only for 48-h mortality in injured patients over 55 [77] and has no validated cut-off, so the number could not be judged.
Age and sex set typical blood pressure: when you change age or sex by hand, SBP and DBP are set to the mean of US adults of that age and sex (NHANES 2001–2008, all participants) [78], interpolated between the published age groups 18–39, 40–59 and 60+.
Systolic pressure rises with age while diastolic falls after about 50 [79]. Scenarios never trigger it, and you can still change SBP and DBP afterwards. Resting heart rate is not changed: it stays near 72 beats/min at all adult ages [80].
These are teaching calculations, not prescriptions.
Formulas (each choice is kept in this browser; the first entry of each list is the default):
QTc: Framingham QT + 154·(1 − RR) [82] is the default because Framingham and Fridericia QT/RR⅓ [89] corrected for rate best and Bazett QT/√RR corrected worst in 6 609 adults in sinus rhythm below 90 bpm [88]; Hodges QT + 1.75·(HR − 60) is also offered [88].
The QT shown on the HR tile is the QT the ECG model places for the last supraventricular beat, not a value measured from the trace; it is blank for ventricular beats, VF and asystole and outside RR 0.3–2 s.
The model's QT follows Framingham, so Framingham QTc stays near 400 ms at every rate while Bazett rises at fast rates: the over-correction reported in [88].
BSA: Mosteller [13], DuBois & DuBois [90] or Haycock [91] (the last was also validated in infants and children).
Max HR: Tanaka 208 − 0.7 × age [75], Gellish 207 − 0.7 × age [92], or the older 220 − age, which Tanaka et al. showed underestimates maximal HR in older adults [75].
NIBP MAP shown: the oscillometric MAP (cuff pressure at the largest oscillation, what oscillometric monitors measure) or the one-third rule DBP + (SBP − DBP)/3 for comparison. Both stay on the NIBP tile; the choice sets the number in brackets. Alarms are not affected.
The banner above the monitor tiles repeats the profile numbers that matter at the bedside: BMI and its adult category, BSA, the NHANES mean blood pressure for this age and sex [78], the predicted maximal HR and, if switched on, the shock index.
Models used (summary)
The full derivation, parameters and assumptions are in TECHNICAL_REPORT.md. All models are simplified teaching models.
None of them is a validated physiological or device model.
ECG: McSharry dynamical model
A point moves on a limit cycle in the (x, y) plane with angular speed ω = 2π/RRi. Its height z is pushed by five Gaussian events, P, Q, R, S and T:
ż = − Σi∈{P,Q,R,S,T} ai Δθi exp(−Δθi² / 2bi²) − (z − z0), Δθi = (θ − θi) mod 2π
Each beat interval RRi is 60/HR plus Gaussian jitter (SD set by the variability control). Irregular mode draws it uniformly within ±35 %.
Noise, baseline wander and mains interference are added. Then the display filter (band-pass, notch) is applied.
A simplified Pan–Tompkins detector (derivative, square, moving-window integral, adaptive threshold) finds the R peaks for the HR estimate.
The ECG is never generated from a measured heart rate.
Pulse oximetry: ratio of ratios
Iλ(t) = I0 exp(−kλ · PI · s(t)) → R = (ACred/DCred) / (ACIR/DCIR) → SpO₂ ≈ 110 − 25 R
The linear calibration line is a textbook approximation. Real oximeters use empirical calibration curves.
The signal quality index (SQI) measures how consistent R stays over 4 one-second windows. Motion adds a common-mode artifact that pulls R toward 1 (SpO₂ ≈ 85 %).
NIBP: oscillometric method
The cuff inflates above the expected systolic pressure, then deflates linearly. The oscillation amplitude of each beat follows the slope of an arctangent pressure–volume curve of the artery at transmural pressure Part − Pcuff.
MAPosc is the cuff pressure at the maximum amplitude Am. SBP is where the amplitude falls to Ks·Am above the maximum. DBP is where it falls to Kd·Am below the maximum.
MAPformula = (SBP + 2·DBP) / 3 PP = SBP − DBP (derived values, not measured)
Respiration: impedance pneumography
The transthoracic impedance changes with lung volume. A phase oscillator at RR/60 Hz drives the breath waveform, and a cardiogenic component and noise are added.
A band-pass filter and hysteresis threshold detect breaths. If no breath is detected for the apnea delay, apnea is declared.
Temperature: first-order probe
dTprobe/dt = (Ttrue − Tprobe) / τ
Capnography: time-based CO₂ waveform
The same breath oscillator drives the capnogram. During inspiration CO₂ falls to the inspired level FiCO₂ (phase 0). During expiration it stays at FiCO₂ for the dead space (phase I),
rises with time constant τ (phase II) and ends on a slightly rising plateau (phase III). EtCO₂ is the maximum of each breath.
c(v) = FiCO₂ + (Pplateau − FiCO₂) · (1 − e−v/τ) / (1 − e−1/τ), τ = 0.035 + 0.35 · obstruction
Pplateau falls with cardiac output: with no perfusion (V-Fib, asystole) little CO₂ reaches the lungs, so EtCO₂ drops. Airway obstruction slows phase II ("shark fin").
Rebreathing lifts the inspired baseline. These are qualitative teaching shapes. Gas sampling delay and water traps are not modelled.
Invasive arterial pressure: second-order transducer
The fluid-filled catheter and transducer act as a second-order system with natural frequency fn and damping ratio ζ (Gardner 1981):
ẍ = ωn² (Part − h·0.7356 − x) − 2ζωn ẋ, ωn = 2π fn
Optimal: fn 20 Hz, ζ 0.6. Under-damped: 6 Hz, ζ 0.1 (systolic overshoot, ringing). Over-damped: 4 Hz, ζ 1.5 (blunted systolic, raised diastolic).
The mean pressure is almost unchanged in each case. h is the transducer height above the heart in cm; 1 cm of water ≈ 0.7356 mmHg. A line open to air reads 0.
Rhythm analysis: rule-based teaching analyser
The monitor band-passes the acquired ECG (0.5–40 Hz) and measures each detected QRS width. It then applies simple rules every second:
almost flat trace → asystole; no QRS for 4 s on a busy trace, or wide chaotic complexes → V-Fib; the last 4 complexes wide above 100 bpm → V-Tach; the last 8 narrow, very regular and above 150 bpm → SVT (P waves are not checked, so a fast sinus rhythm gets the same label);
narrow-to-narrow RR coefficient of variation above 0.12 → irregular; any wide complex in the last 60 s → PVCs. The first 8 s are "learning".
The thresholds were tuned on this simulator's own waveforms. This is not a validated arrhythmia algorithm (arrhythmia performance is tested per ANSI/AAMI EC57 on annotated databases such as MIT-BIH and AHA) and it gives no diagnosis.
Main components of a bedside monitor
This is a generic block diagram from the textbook literature (Webster, Medical Instrumentation; Webster, Design of Pulse Oximeters; Allen 2007; Forouzanfar et al. 2015). It describes no specific product and claims no device specifications.
- ECG channel: skin electrodes and lead wires → protected, isolated input → instrumentation (differential) amplifier with high common-mode rejection → band-pass and optional mains notch filter → analogue-to-digital converter (ADC) → QRS detector → heart rate.
- Impedance respiration: a small high-frequency carrier current passes through the ECG electrodes. The impedance change caused by breathing is demodulated, filtered and counted as breaths.
- SpO₂ channel: a probe with a red LED, an infrared LED and one photodiode → transimpedance amplifier → red and IR signals separated by time multiplexing → AC/DC extraction → ratio of ratios R → calibration curve → SpO₂ and pulse rate.
- NIBP channel: cuff, air pump, deflation valve and pressure transducer → the controller inflates, then deflates → the oscillations on the cuff pressure are extracted → envelope → MAP, then SBP and DBP by ratio rules. An over-pressure limit stops inflation.
- Temperature channel: thermistor probe in a bridge or divider → ADC → linearisation to °C. The probe responds with a time lag.
- Processing and output: processor; display of waveforms and numerics; alarm system with limits, priorities, delays and audio/visual signals (IEC 60601-1-8); trend storage; network or serial interface to a central station.
In this app each channel is a module in src/sim/. Each sensor control (noise, mains, contact, motion, probe state, time constant) acts on the stage of the chain that it names.
Simplifying assumptions
- One ECG lead with a fixed morphology. The arrhythmias are six teaching patterns (AF, SVT, PVCs, V-Tach, V-Fib, asystole). Blocks, flutter and paced rhythms are not modelled.
- Perfusion is one number between 0 and 1. It falls when no effective beat occurs and drives the arterial pressure, the pulse and the EtCO₂.
- The pulse has a fixed shape and arrives 0.20 s after the R wave. ECG, PPG, pressure and respiration share the same beat times.
- The PPG uses two wavelengths and a linear calibration. Venous pulsation, ambient light and dyshaemoglobins (COHb, MetHb) are not modelled.
- Breathing is regular, with I:E = 1:2.
- NIBP uses an arctangent artery model, linear deflation and fixed ratios. The cuff and limb tissue are not modelled.
- Parameters are independent: lowering SpO₂ does not raise HR. Alarm limits and delays are illustrative defaults.
Engineering limitations
- Motion: motion pulls R toward 1, so the displayed SpO₂ drifts toward about 85 % while the SQI falls. At high motion the NIBP measurement fails with a motion message.
- Fixed-ratio NIBP: SBP and DBP are estimates, not measurements. In the hypotension preset the DBP estimate can stay just above the alarm limit.
- Detector: the QRS detector has no search-back. Dropouts and heavy noise can cause missed beats and a wrong HR.
- Not represented:
- oximeter bias from skin pigmentation and low perfusion (FDA 2021)
- cuff-size errors
- validated arrhythmia detection (the analyser here is illustrative)
- pacemaker pulses
- catheter whip, air bubbles and clots in the arterial line
- sidestream gas-sampling delay
- electrosurgical interference
- electrical safety and isolation
The full lists are in TECHNICAL_REPORT.md §8–9. The observed test results are in TEST_REPORT.md.
Data provenance
Every value is an observation with a source: simulated derived
device imported user. It also has a quality flag (ok, low-quality, missing, invalid, artifact) and a provenance record.
Simulated data and real (device, imported, manual) data are never mixed in one series.