Technical appendix
What this page actually computes
This is a complete description of the model behind this simulator. It is a deterministic teaching simulation: every curve is computed from the slider values by the equations below, in your browser, with no accounts and nothing sent anywhere; the only things it keeps are your light-or-dark theme choice (saved in your own browser) and the slider state in the page’s own URL. It is not a bolus calculator, not a medical device, and not clinically validated — it exists to make the logic of the Warsaw Method visible.
1 · Dose logic (the Warsaw Method)
The method implemented here is the fat–protein unit (FPU) dual-wave algorithm developed by Prof. Ewa Pańkowska and colleagues in Warsaw, Poland. The dose math is:
Wave 1 (now) = Carbs ÷ ICR + max(0, (BG − Target) ÷ ISF)
FPU = (Fat × 9 kcal/g + Protein × 4 kcal/g) ÷ 100
if FPU < 1.0 → no second wave
Carb equivalent = FPU × 10 g
Wave 2 (extended) = (Carb equivalent × Adjustment% ) ÷ ICR
The correction is clamped at zero (a below-target glucose never reduces the carb dose here), and this tool takes no insulin-on-board input — it models a single meal starting from zero active insulin. The second wave's length comes from the standard FPU lookup table, or from the manual override slider (the override changes only how the insulin is delivered; the food still arrives on the table's schedule):
The suggested pre-bolus is a smoothed ramp on current glucose: 0 min below 80 mg/dL, 8 + ((BG − 80) ÷ 120) × 12 min from 80–200, capped at 20 min above 200. (Glucose trend arrows are not modeled.)
2 · Insulin activity curve
Insulin action uses the two-parameter exponential activity model popularized by the open-source automated-insulin-delivery community (oref0/OpenAPS and Loop), with duration td set by the "insulin duration" slider (3–6 h) and peak time tp = min(75 min, 0.4 × td):
τ = tp · (1 − tp/td) ÷ (1 − 2·tp/td)
a = 2τ/td
S = 1 ÷ (1 − a + (1 + a)·e^(−td/τ))
activity(t) = (S/τ²) · t · (1 − t/td) · e^(−t/τ) for 0 ≤ t ≤ td
activity(t) integrates to 1 over the duration, so each unit is fully "spent." The glucose-lowering rate of a dose is units × activity(t) × ISF in mg/dL per minute. Wave 1 is a single dose at t = 0. Wave 2 has two delivery modes: pump drip models a steady infusion (dose ÷ length, in 2-minute steps) with each micro-dose following the same activity curve — numerically, a convolution — mirroring a pump's extended/square-wave bolus. Pen shots models the same total as discrete injections using one common approximation: waves of 4 hours or less become a single injection of the full wave-2 amount 90 minutes after eating; longer waves split in half, at 60 minutes and at the wave's halfway point. This split rule is a teaching heuristic, not a published protocol — real pen strategies vary and pens dose in whole or half units.
3 · Food absorption curves
Carbs begin absorbing at the first bite (t = pre-bolus) with a gamma-shaped curve, c(t) ∝ t · e^(−t/τ), normalized to deliver 100% of the grams. The glycemic-index control sets τ: fast = 28 min, medium = 40 min, slow = 58 min — so "fast" peaks sooner and higher and clears earlier, while "slow" spreads the same grams into a longer, flatter rise. The three settings are illustrative bands, not a lookup of any published GI table, and they change the shape only — never the total grams absorbed.
Fat and protein deliver their carb equivalent (FPU × 10 g) as a raised-cosine hump starting 60 minutes after the first bite and spread over the FPU table's duration, scaled by the "body's response" slider (0–100%, default 50%). That slider is the model's stand-in for individual variation in gluconeogenesis and delayed gastric emptying — it is a hypothesis knob, not a measured quantity. Each absorbed gram (fast or slow) raises glucose by ISF ÷ ICR mg/dL, the standard carb-sensitivity identity.
4 · The glucose trace
BG(t + Δt) = BG(t) + [ carb_rate(t) + fpu_rate(t) − wave1_rate(t) − wave2_rate(t) ] · Δt
Forward-Euler integration on a 2-minute grid over a 10-hour window, seeded from the "example glucose" slider. No basal insulin, liver glucose output, dawn effect, exercise, stress, or counter-regulation is modeled — the trace shows only this meal against these doses, which is exactly what makes the two-wave logic legible.
The variability cone is the shaded band around the line. It widens with how much food has landed and how far into the meal you are — ± min(40, 0.15 × grams-of-glucose-delivered-so-far × √(elapsed fraction)) mg/dL. It is a deliberately simple way to draw "a prediction this far out is a guess," not a confidence interval, a standard deviation, or anything derived from real CGM data. Read it as "roughly this wide," never as a number.
The four live stats above the chart read straight off the simulated curve over the full ten hours: peak is its highest point, lowest after eating is its minimum from the first bite onward, and in range is the share of the ten-hour window spent between 70 and 180 mg/dL. They describe the model's curve, not a person's day.
The dashed "carbs-only ghost" is the identical simulation with wave 2 removed: same food, same wave 1 (carbs + correction), zero extended insulin. It answers "what would a standard single bolus have done to this exact meal?" and appears only when the meal earns a second wave.
5 · Guardrails in the simulation
- A starting glucose below 60 mg/dL shows a treat-the-low-first message, and 60–70 shows a caution. Both describe the value on the slider, not the simulated curve — the curves are always drawn either way.
- A model total above 25 units shows a sanity warning. Nothing is capped and nothing halts; the warning is advisory.
- The integrated curve is bounded to 20–600 mg/dL, so an extreme slider combination can never display a physiologically impossible number. If a curve flattens against either bound, the settings — not the body — are what ran out of room.
- Negative inputs and negative dose components are clamped to zero.
6 · Interface behaviors
- Units: all internal math runs in mg/dL. The mmol/L toggle converts displayed values by dividing by 18 (and the in-range band becomes 3.9–10.0 mmol/L); it changes nothing in the computation.
- Scenario buttons only set the sliders to preconfigured values and show a caption — they use no extra logic, so every scenario can be reproduced or undone by hand. The five failure scenarios mirror the four post-meal CGM patterns (bolus too late, bolus too early, dose too small, dose too large) plus the Warsaw-specific one, so what you see here maps onto a real trace. Because carb sensitivity in this model is ISF ÷ ICR, the carb ratio is a physiology setting rather than a dose-size knob — so the under- and over-dosing scenarios are built from the coverage-versus-response mismatch on the slow wave.
- Clicking a legend key hides that layer on the tug-of-war chart and rescales the axis to whatever remains; the last visible layer can't be switched off.
- Share links: the full slider state — including glycemic index and the chart toggles — is encoded in the URL fragment (the part after #) and updated as you drag. The fragment is read once on load; nothing is transmitted or stored anywhere — the "copy a link" button just copies the current URL.
7 · Known simplifications
Real absorption varies meal to meal and person to person (gastric emptying, activity, alcohol, illness, hormones, stress); insulin sensitivity drifts across the day; fat can also cause temporary insulin resistance beyond what a carb-equivalent captures; and combination meals interact in ways no fixed curve reproduces. Basal insulin, insulin on board from earlier doses, exercise, illness and hormones are all absent from this model. Treat every number on this page as an illustration of relationships — what gets bigger, what gets longer, what moves earlier — never as a dose.
8 · Sources
FPU concept, 100-kcal unit, ×10 g carb equivalence, duration table, and the 50% starting factor: the pump-therapy research of Pańkowska et al. (Warsaw, Poland). Exponential insulin activity model: the open-source AID community (oref0/OpenAPS, Loop). Implementation, plain-language framing, and food-curve shapes: the Juicebox Podcast — simplifications are ours, not theirs. Hear the thinking behind this tool in Diabetes Pro Tip 1012: Fat and Protein and 1008: The Perfect Bolus.