A walkthrough of the real calculator, followed by a complete account of the mathematics and the population models it uses, each tied to the paper it came from. Every screenshot is a synthetic demo patient, never a real one. This is orientation, not clinical advice — the tool is decision support, and every number it produces still wants a clinician's judgement.
Inputs on the left, answers on the right. Two modules across the top: Trough-Based for deterministic dosing, and AUC Precision for Bayesian fitting once you have levels. Saved profiles work in both — save from either and loading fills both, so a patient is entered once. Nothing leaves the browser: there is no server and no network call.
Age, sex, height, weight and creatinine. The tool derives ideal and adjusted body weight and shows the creatinine clearance it will use, naming the weight basis so you can see which one it chose. The creatinine is used exactly as entered — it is never rounded up. If cystatin C is available, entering it surfaces a creatinine/cystatin discordance check, which is the honest answer to the low-muscle-mass problem that rounding was invented to paper over.
A starting regimen from population pharmacokinetics before any level exists. Choose the clearance and volume models on the right; the panel underneath states the provenance of whichever you pick. Expect roughly ±35% uncertainty on exposure at this stage — that is what "no levels yet" means, and the tool says so rather than implying precision it does not have.
Enter what the patient actually received — every dose, its infusion duration, and the real administration time — then the measured level and when it was drawn. Times matter more than people expect: the fit is only as good as the timestamps. Rows that are started but incomplete are reported rather than silently dropped.
The fit. Read it top-down: the regimen the tool believes the patient is on (with its confidence, and whether it detected a change of interval), then the fitted clearance and volume beside the population values, then the recommendation. The banner in this example reports a genuine q12h → q8h transition — detected from the two most recent intervals rather than from whichever interval appeared most often. If you know the intended order, set it in Current intended regimen; that steers the projection and never alters the data the fit consumes.
The solid line is this patient; the dashed line is what the population model predicted before their levels were known. The gap between them is what the measurement bought you. Points are measured levels, vertical marks are doses with the interval between them annotated, and the shaded band is a trough reference — not a target. Hover anywhere on the curve to read the fitted concentration at that instant, the clock time, and how long it has been since the last dose.
Doses and levels are entered as full timestamps everywhere in the tool — never a bare clock reading. This is not tidiness; it is the difference between a correct answer and a confidently wrong one.
Two-level sampling routinely spans midnight. A dose at 10:22 and a level at 10:38 the next morning are 24.3 hours apart, but from clock readings alone that is indistinguishable from 16 minutes. Earlier versions of this tool resolved the ambiguity by assuming the same day and adding 24 hours only when the result went negative, which folds every interval into the range 0–24 h.
That has two consequences, and the quieter one is the dangerous one. When the second level wraps below the first, the solver refuses and says so. But when both levels fall on a later day they shift by the same 24 hours, the log-linear slope between them is unchanged, and the elimination rate still comes out right — while the back-extrapolation to the peak, which uses the absolute time, is a full day early. Volume of distribution then comes out several-fold wrong with nothing on screen to suggest it. A dose at 08:00 with levels at 12:00 and 18:00 the next day gave a Vd of 75 L where the truth was 13 L.
Each field now carries its own date, and the tool prints the elapsed interval back to you — 1d 0.3h (total 24.3h) after dose start — so you can confirm it read the timestamps the way you meant them before you trust anything downstream. A level dated before its dose is reported as an error rather than silently absorbed.
The plot exists so you can estimate a concentration at a time point. Its axes are built for that, and a few of its choices are deliberate enough to be worth stating.
Ticks are placed at half the dosing interval, so there are always seven of them and every dose boundary falls on one — at Q6H they land on 0, 3, 6, 9, 12, 15 and 18 h; at Q48H on 0, 24, 48 and so on. You can therefore read the trough directly off a gridline rather than interpolating toward it. The vertical terracotta rules mark where each dose is given.
This replaced a fixed 8-hour tick that aligned with no dose boundary at Q6H, Q12H, Q18H, Q24H, Q36H or Q48H, and drew nineteen overlapping labels at Q48H.
The vertical range is chosen to include the curve, the target band, and any measured level — not just the curve. That matters for a low-dose regimen in a fast clearer: if the axis followed the curve alone, a 10–20 mg/L band would be painted off the top of a plot whose peak was 8 mg/L, and the band would read as "everything above 10 is on target." Gridlines are placed on round values at a roughly constant density whatever the scale.
The band is drawn from the trough range you entered, and labelled with those bounds — it is not a fixed 10–20. It is shaded for orientation only: the 2020 guideline withdrew trough as a target (Rec 3, A-II) and AUC24 governs. It stays on the chart because a trough is still the value a level actually measures.
| Mark | Meaning |
|---|---|
| Rose ×, with a value | A measured level. The only real number on the chart; everything else is a model. Drawn above the curves so nothing hides it. |
| Solid terracotta line | This patient's fitted concentration-time curve. |
| Dashed neutral line | What the population model predicted before the levels were known. The gap between the two is what the measurement bought you. |
| Solid purple line | Projection under doses that have not been given yet. |
| Amber and purple dots | Predicted peak (end of infusion) and trough (end of interval). |
| Shaded band | Your trough reference range, labelled with its bounds. |
Markers are drawn on the curve, not near it — the curve is sampled at the end of infusion and at each interval boundary specifically so the peak dot sits on the line rather than above the corner the polyline would otherwise cut. If a marker ever appears off the curve, that is a bug, not rounding.
In Random Level mode the level is fitted against single-dose decay while the chart draws a steady-state profile. These are different models, so the plotted point and the drawn curve will not coincide, and that is expected rather than an error. Read the fitted parameters, not the visual fit.
The tool computes exposure. It does not choose your dosing interval, and the reason is arithmetic rather than modesty.
At steady state the area under the curve over 24 hours is simply the total daily dose divided by clearance:
AUC24 = dose x (24/tau) / CL = total daily dose / CLThere is no interval term in it. 500 mg every 12 hours and 1000 mg every 24 hours deliver exactly the same exposure, and so does 2000 mg every 48 hours. Any rule that ranks regimens on how close their AUC24 sits to a target is therefore blind to the interval by construction; whichever interval happens to reach a daily dose nearest the target wins, and with doses rounded to 250 mg that is decided by rounding rather than by pharmacology. The rounding is not even-handed either — one 250 mg step moves AUC24 six times less at Q48H than at Q8H, so a long interval can always land closer.
Rather than hide that behind a tuned preference score, the tool shows the whole picture. The exposure matrix lays out every dose against every interval, shades each cell against the 400–600 mg·h/L band, strikes through anything that breaches a hard safety limit, outlines the recommended cell, and lets you click any other one to see its full profile. The AUC values repeat down the diagonals, which is the point: those regimens are exposure- equivalent.
What does change with the interval is the shape — peak and trough. Those are yours to weigh against renal trajectory, how long you expect the regimen to stand, infusion-related tolerability and practicality on the ward. The tool gives you the numbers for each; the judgement is not something it can derive from an AUC target.
The single recommendation is still shown, because a starting point is useful. Treat it as one admissible cell among several rather than as a ranking the model has earned.
Everything below is implemented in the shipped file and covered by an automated suite that runs the real engine — 101 unit and regression tests, 21 simulation checks, and 40 regimen-detection cases. Fifteen of those run the actual chart renderers and assert on what they draw.
Ideal body weight. At or above 60 in (152.4 cm), Devine (1974):
IBW = 50 (male) or 45.5 (female) + 2.3 x (height_in − 60) Below 60 in, Devine extrapolates downwards and understates IBW, so the GlobalRPH BMI method is used instead — with the target BMI derived from the Devine anchor rather than chosen:
IBW = (50 ÷ 1.524²) x height_m² = 21.53 x height_m² (male)
IBW = (45.5 ÷ 1.524²) x height_m² = 19.59 x height_m² (female) Deriving the target from the anchor is what makes the two methods meet: IBW is continuous and monotonic across 152.4 cm. Substituting round numbers such as 21.5 / 22.0 — a different method entirely (Tokunaga 1991) — breaks the join and makes a 152.3 cm woman weigh more than one at 152.5 cm.
Adjusted body weight — AdjBW = IBW + 0.4 x (TBW − IBW), used for creatinine clearance when total weight exceeds IBW by more than 20%. Where actual weight is below the selected basis, actual weight wins.
Creatinine clearance — Cockcroft-Gault, on the measured creatinine:
CrCl = ((140 − age) x weight) ÷ (72 x SCr) x 0.85 if female No rounding of low creatinine. Rounding up in the elderly under-doses measurably: in 56 patients aged ≥65 with baseline SCr <1, rounded creatinine missed measured troughs by 8.84 mg/L against 4.54 mg/L for the actual value, and 92.9% came out subtherapeutic (Drugs R&D 2017;17:463-70). The one exception is internal to the Goti model, which was estimated on truncated creatinine and so must be fed the same transformation — that never touches the creatinine clearance shown on screen.
With R0 = dose ÷ t_inf, ke = CL ÷ V, interval tau:
C_peak = (R0 ÷ (ke·V)) · (1 − e^(−ke·t_inf)) ÷ (1 − e^(−ke·tau))
C_trough = C_peak · e^(−ke·(tau − t_inf)) During the infusion the residual from the previous interval must be carried forward:
C(t) = (R0 ÷ (ke·V)) · (1 − e^(−ke·t)) + C_trough · e^(−ke·t) 0 ≤ t ≤ t_inf
C(t) = C_peak · e^(−ke·(t − t_inf)) t > t_inf Dropping that second term is a real and easy mistake — it agrees with the correct form at the end of the infusion, so it looks right, but it returns zero at t = 0, implying no drug present immediately before a dose at steady state. It shipped here until September 2026 and was caught by external review.
AUC_24 = (dose x 24 ÷ tau) ÷ CL Exact at steady state and independent of the compartment model — which is why it, not the trough, is the quantity the tool optimises against. A trapezoidal form (linear across the infusion, log-linear across elimination) is also implemented; the two agree to within 0.31% worst case.
Two levels, no prior — Sawchuk-Zaske. The elimination rate comes straight from the slope between two post-infusion concentrations:
ke = ln(C1 ÷ C2) ÷ (t2 − t1) Volume then comes from back-extrapolating to the peak — and here where in the course the levels were drawn changes the answer. The single-dose form assumes nothing was left over from a previous dose:
V = (R0 ÷ (ke·C_peak)) · (1 − e^(−ke·t_inf)) first dose
V = (R0 ÷ (ke·C_peak)) · (1 − e^(−ke·t_inf)) ÷ (1 − e^(−ke·tau)) steady state Elimination is basis-independent — accumulation does not change a log-linear slope. Volume is not. Treating steady-state levels as first-dose levels attributes the drug already in the body to a smaller volume: for a patient with ke 0.0866 and V 52 L on 1000 mg q12h, V comes back as 33.6 L (−35%) and AUC24 as 687 against a true 444 — a 55% over-read, which would argue for reducing the dose of a patient already at target. The calculator therefore asks which it is rather than assuming.
Bayesian MAP — minimise the Burton (1985) objective over the individual deviations eta:
OBJ = Σ (eta_i² ÷ omega_i²) + Σ ((C_pred − C_obs)² ÷ SE²)
The first sum is the price of departing from the population; the second is the price of disagreeing with
the measurements. Minimising their total is what "bend towards the patient, but only as far as the data
justifies" means arithmetically. Parameters are exponential — CL = CL_pop · e^(eta_CL) — so they
stay positive. The search is Nelder-Mead simplex, in two dimensions for one-compartment models and three
for two-compartment.
Concentrations follow a bi-exponential: a fast distribution phase then a slow terminal phase, with the macro-constants alpha and beta obtained from the micro-constants k10, k12, k21. Steady state is reached by superposition of repeated doses — and the number of cycles required is derived from the terminal half-life rather than assumed:
beta = ((k10 + k12 + k21) − √((k10 + k12 + k21)² − 4·k21·k10)) ÷ 2
cycles = ceil(10 x (ln2 ÷ beta) ÷ tau), clamped to [12, 400] A fixed 12 cycles is not steady state when clearance is low. At CrCl 10 a Goti patient has a terminal half-life near 110 h, so twelve 12-hourly cycles covers about 1.3 half-lives and reads the trough roughly 40% low — in exactly the renal-impairment patients where accumulation is the danger.
Four Bayesian priors and four deterministic model pairs. Every parameter below was checked against the primary source; where a coded value disagreed with its paper, the paper won.
| Model | Structure | Typical values | Between-subject | Residual | Source |
|---|---|---|---|---|---|
| Buelga 2005 Haematological malignancy, n=215 | 1-compartment | CL (L/h) = 1.08 x CLcr (L/h); V (L) = 0.98 x TBW | omega 28.16% (CL), 37.15% (V), exponential | sigma 3.52 mg/L, additive | Buelga DS et al. Antimicrob Agents Chemother 2005;49(12):4934-41 verified: verbatim |
| Goti 2018 Hospitalised adults incl. haemodialysis, n=1,812 | 2-compartment | CL = 4.5 x (CrCl/120)^0.8 x 0.7^DIAL; Vc = 58.4 x (WT/70) x 0.5^DIAL; Vp = 38.4; Q = 6.5 | BSV %CV 39.8 / 81.6 / 57.1 (CL / Vc / Vp) | 22.7% proportional + 3.4 mg/L additive | Goti V et al. Ther Drug Monit 2018;40(2):212-21 (+ erratum 2019;41(4):549) verified: 16 of 16 parameters |
| Goti 2018 — HD The dialysis arm of the same model | 2-compartment | As above with DIAL = 1: CL x 0.7 and Vc x 0.5 | as Goti | as Goti | Goti V et al. Ther Drug Monit 2018;40(2):212-21 verified: as Goti |
| Hughes 2024 Class 3 obesity ONLY — BMI ≥ 40 (median 46.3, range 40–70.3) | 2-compartment, FFM-scaled | CL = 5.09 x (CrCl_FFM/100)^0.887; Vc = 64.9 x (FFM/70); Vp = 66.4 x (FFM/70); Q = 6.36 | BSV %CV 24.9 / 17.8 / 80.3 | 15.6% + 1.2 mg/L | Hughes M-SA et al. Ther Drug Monit 2024;46(5):575-83, Table 2 (nlmixr2) verified: Table 2 exact; one structural defect corrected |
| Model | Clearance | Volume | Provenance |
|---|---|---|---|
| VancoPK | CL (mL/min) = 0.75 x CrCl + 4 | Vd (L) = 0.29 x age + 0.33 x TBW + 11 | Vd: Fewel N. J Clin Pharm Ther 2021;46:1426-32 (verified verbatim). CL: vancopk.com in-house regression, updated Nov 2023 — site documentation, not peer-reviewed. |
| Matzke 1984 | CL (mL/min) = 0.689 x CrCl + 3.66 | 0.72 or 0.89 L/kg by CrCl band, or 0.875 L/kg pooled | Matzke GR et al. Antimicrob Agents Chemother 1984;25(4):433-7. The CL equation is verbatim (r = 0.8807). The Vd split on CrCl is NOT a published covariate — the paper states there was no significant relationship between Vd and CLcr — so a pooled option is offered. |
| Buelga 2005 | CL (L/h) = 1.08 x CLcr (L/h) | 0.98 L/kg TBW | Same model the AUC module uses as its Bayesian prior — the two modules agree exactly. |
| Bauer | per-kg clearance x weight | 0.70 L/kg TBW | Bauer LA. Pharmacotherapy: A Pathophysiologic Approach, 11e, ch. e5. Textbook method; no standalone source paper. |
The tool recommends a model from the patient, but the choice is yours. Two constraints are worth knowing because they are easy to get wrong:
Simulated against the verified Buelga prior, 2,000 patients per level count. These are measured, not asserted, and are quoted at the ~80th percentile:
| Levels | Median error | 80th percentile | 90th percentile | Within ±15% |
|---|---|---|---|---|
| 0 — population only | 18.3% | 35.4% | 45.9% | 42% |
| 1 | 10.3% | 20.9% | 28.3% | 66% |
| 2 | 8.8% | 18.2% | 25.4% | 73% |
| 3 or more | 8.1% | 17.1% | 23.2% | 76% |
The first level buys the most. The tool previously claimed ~±15% at one level; only 66% of simulated patients met that, so the disclosure was re-derived from simulation and now states the percentile it means.
A dose recommendation is filtered before it is offered. The bounds are tiered by how much clinical judgement each requires.
| Tier | Bound | Value | Source |
|---|---|---|---|
| Hard reject dose-domain; cannot be wrong for a clinical reason | Single dose | ≤ 2000 mg | conventional adult per-dose ceiling |
| Total daily dose | ≤ 4500 mg | adult empiric maintenance ceiling | |
| AUC24 absolute | ≤ 700 mg·h/L | AKI risk rises above ~650 (Rybak 2020); Zasowski 2018 | |
| Acceptance band | AUC24 | 400–600 mg·h/L | Rybak 2020 Rec 1 (A-II), assuming MIC 1 mg/L |
| Flags attached to the answer, never used to hide it | Trough warning | ≥ 15 mg/L | AKI risk begins to rise (Rybak 2020) |
| Trough high | ≥ 20 mg/L | upper end of that band; trough ≥18.2 → 3–4× risk | |
| Sub-inhibitory | trough < MIC | part of each interval below the MIC |
Trough is deliberately not a filter. Because the dose is solved from the target exposure, every candidate already sits near the target AUC — so a trough window would not be guarding exposure, it would be silently choosing the dosing interval on rounding arithmetic. The 2020 guideline withdrew trough as a target for the same underlying reason: many different profiles share one trough. When no candidate is admissible the tool refuses and says which bound failed rather than quietly returning a rejected regimen.
The engine, its tests and the full audit record — including the defects found and what they cost — live with the source. The calculator runs entirely in your browser; no patient data is transmitted anywhere.