Extended vs Intermittent Infusion Calculator
Extended vs Intermittent Infusion Calculator
The same dose at the same interval, over 30 minutes and over several hours: how many percentage points of fT>MIC the longer infusion buys, from the exact one-compartment steady-state equations.
Extended against 30-minute infusion
fT>MIC, two infusion times4,000 mg every 8 h, clearance 14 L/h, half-life 0.75 h, MIC 16 mg/L, 30% protein bound, extended infusion over 4 h
The two closed forms, and how they meet
- during the infusion
- with Cinf = D / (T · CL), C(t) = Cinf − (Cinf − Cmin) · e^(−ke t) for 0 ≤ t ≤ T, rising monotonically from Cmin to Cend. So Cend is the interval’s maximum and Cmin its minimum, and C(t*) = MIC gives the crossing t* = ln((Cinf − Cmin) / (Cinf − MIC)) / ke — always a logarithm of a positive number, since Cend > MIC implies Cinf > Cend > MIC
- the time above the MIC
- T>MIC = (T − t*) + min( ln(Cend/MIC) / ke , τ − T ) — the tail of the infusion plus the decay afterwards, capped at the end of the interval. It is τ outright when Cmin ≥ MIC and zero when Cend ≤ MIC
- the degenerate point
- as T → 0, (1 − e^(−ke T)) / T → ke, so Cend → (D/V) / (1 − e^(−ke τ)) — the bolus steady-state peak — and t* → 0, collapsing onto the form the time above MIC calculator uses. The proof sweeps T to 10⁻⁵ hours and asserts the two agree
- free drug
- the dose is scaled by the unbound fraction first, because fT>MIC is a free-drug index and concentration is linear in dose
Worked example
4,000 mg every 8 h, clearance 14 L/h, half-life 0.75 h, MIC 16 mg/L, 30% protein bound, extended infusion over 4 h
Unbound fraction 0.70, so the free-drug-equivalent dose is 2,800 mg; ke = ln 2 / 0.75 = 0.9242 per hour
30-minute arm: free peak 148.11 mg/L, free trough 0.145 mg/L, time above 16 mg/L = 2.86 h of 8, which is 35.8%
4-hour arm: free peak 48.79 mg/L, free trough 1.210 mg/L, time above 16 mg/L = 4.82 h of 8, which is 60.2%
60.2 − 35.8 = 24.4 percentage points gained, for the same milligrams at the same interval
Set the extended duration to 0.5 h and the answer is exactly 0.0 — the two arms are then the same regimen, which is the degenerate point a wrong implementation would pass
Move the MIC one doubling dilution either way and both figures move, and so does the gain: at 8 mg/L it is 72.4% against 45.5%, a gain of 27.0 points, and at 32 mg/L it is 42.2% against 25.9%, a gain of 16.4. The direction is stable across the bracket but the size is not
What a longer infusion does to the curve, at the page’s defaults
| Infusion time | Free peak (mg/L) | Free trough (mg/L) | fT>MIC at 16 mg/L |
|---|---|---|---|
| 0.5 h | 148.11 | 0.145 | 35.8% |
| 1 h | 120.70 | 0.187 | 38.7% |
| 2 h | 84.30 | 0.329 | 45.2% |
| 4 h | 48.79 | 1.210 | 60.2% |
| 6 h | 33.22 | 5.232 | 78.3% |
Where the comparison stops mattering
| Situation | What happens |
|---|---|
| The MIC is well below the short-infusion trough | Both arms give 100% fT>MIC and the difference is zero. A longer infusion cannot improve on a target already fully met |
| The MIC is above the extended-infusion peak | Both arms give 0% and the difference is zero — and in this case the longer infusion, with its lower peak, is the first to fall below |
| The extended duration equals 30 minutes | The two arms are the same regimen and the difference is exactly zero — the degenerate point, where a wrong implementation also returns zero |
| The half-life is long relative to the interval | The trough is already high and fT>MIC is near 100% on both arms, so the gain shrinks — which is why a once-daily long-half-life agent gains little from prolonging its infusion |
The same milligrams, a different curve
Two regimens delivering the same dose at the same interval have the same 24-hour area under the concentration-time curve: area is total dose divided by clearance, and neither changes. Lengthening the infusion changes the shape — the peak falls, the trough rises, the curve spends longer in the middle. For a drug whose index is time above a threshold rather than height reached, that reshaping is free pharmacodynamic gain, worth 24 percentage points of fT>MIC at this page’s defaults.
The arithmetic is exact, and it is the one place in this category where the closed form is not obvious. During a zero-order infusion the concentration climbs towards the value an unending infusion would reach, starting from the trough the previous dose left; afterwards it decays first-order. Both phases are monotonic, so the curve crosses the MIC at most twice in an interval — once on the way up and once on the way down — and solving for each crossing and adding the segments gives the time above the MIC in closed form. As the infusion time shrinks to nothing the expression collapses onto the simple bolus form, which is both a reassurance and the test that catches a wrong implementation: a formula that happens to agree at a 30-minute infusion but is wrong in structure parts company from the bolus form as the infusion shortens.
The clinical evidence is less emphatic. Shea and colleagues’ 10,000-patient Monte Carlo simulation against a 50% fT>MIC target showed prolonged piperacillin-tazobactam infusions reaching the target at MICs where short infusions did not, though none managed it at 64 mg/L. The randomised evidence arrived in 2024. BLING III randomised 7,031 critically ill patients with sepsis to continuous or intermittent piperacillin-tazobactam or meropenem and found 90-day mortality of 24.9% against 26.8%, an unadjusted odds ratio of 0.91 (95% CI 0.81 to 1.01, P = 0.08) that did not reach significance, with a prespecified adjusted odds ratio of 0.89 (0.79 to 0.99, P = 0.04). Its companion meta-analysis of 18 trials and 9,104 participants gave a relative risk of 0.86 (95% credible interval 0.72 to 0.98) with a 99.1% posterior probability of lower mortality. So the direction is consistent and the largest single trial was not significant on its primary unadjusted analysis.
Two limits on reading this page. It holds the interval fixed, while real protocols usually change the interval and the infusion time at once, which mixes two effects. And the model assumes one compartment, first-order elimination and steady state, while in critical illness the volume of distribution expands and clearance may be augmented or collapsed — so a population clearance can be badly wrong in the patient who most needs the calculation. This page does not hold a breakpoint table. EUCAST and CLSI publish them, they are revised two or three times a year, and the laboratory that issued your report has already applied its own version. Take the MIC and the interpretive category from the report; this page does the arithmetic that sits on top of them. The dose itself belongs to the maintenance dose calculator and to whoever is prescribing.
Frequently asked questions
Why does a longer infusion increase fT>MIC?
It reshapes the concentration curve without changing the area under it. A longer infusion lowers the peak and raises the trough, and fT>MIC counts how long the curve stays above the MIC, not how high it climbs. At this page’s defaults the free peak falls from 148 to 49 mg/L, the free trough rises from 0.145 to 1.21 mg/L, and fT>MIC rises from 35.8% to 60.2%.
Does the total daily dose change?
No, and that is the point. Both arms use the same dose at the same interval, so the daily total and the 24-hour AUC are identical and the gain comes from the shape of the curve. An AUC-driven agent such as vancomycin would gain nothing at all from the same change.
When does a longer infusion not help?
At both extremes. If the MIC is below the trough of the short infusion, both arms already spend the whole interval above it and the difference is zero. If the MIC is above the peak of the extended infusion, both arms spend none of it above and the difference is zero — and in that case the lower peak of the longer infusion is a disadvantage. The gain is largest when the MIC sits in the middle of the curve.
Does extended or continuous infusion improve survival?
The evidence points that way without settling it. BLING III, in 7,031 critically ill patients, found 90-day mortality of 24.9% against 26.8% — an unadjusted odds ratio of 0.91 (0.81-1.01, P = 0.08), not significant, with a prespecified adjusted 0.89 (0.79-0.99, P = 0.04). Its companion meta-analysis of 18 trials gave a relative risk of 0.86 (credible interval 0.72-0.98).
What should I enter for clearance and half-life?
Clearance in L/h and the elimination half-life in hours; the volume of distribution is derived as clearance times half-life divided by ln 2. Piperacillin’s label gives 0.7 to 1.2 hours and meropenem’s about 1 hour. In critical illness both parameters move, often day to day, which is the main limitation of any such calculation.
Why is the comparator fixed at 30 minutes?
It is the conventional short infusion for the beta-lactams, and fixing it keeps the page to one variable. Setting the extended duration to 0.5 hours makes the arms identical and the answer exactly zero — the degenerate point, where a transposed implementation also returns zero, so the proof sweeps the infusion time to the limit instead.
Related calculators
References
- Berry AV, Kuti JL. Pharmacodynamic thresholds for beta-lactam antibiotics: a story of mouse versus man. Front Pharmacol. 2022;13:833189. Open access; source for the murine %fT>MIC thresholds and for the human studies set against them.
- Dulhunty JM, Brett SJ, De Waele JJ, et al; BLING III Study Investigators and the ANZICS Clinical Trials Group. Continuous vs intermittent beta-lactam antibiotic infusions in critically ill patients with sepsis: the BLING III randomized clinical trial. JAMA. 2024;332(8):629-637.
- Abdul-Aziz MH, Hammond NE, Brett SJ, et al. Prolonged vs intermittent infusions of beta-lactam antibiotics in adults with sepsis or septic shock: a systematic review and meta-analysis. JAMA. 2024;332(8):638-649.
- Shea KM, Cheatham SC, Smith DW, Wack MF, Sowinski KM, Kays MB. Comparative pharmacodynamics of intermittent and prolonged infusions of piperacillin/tazobactam using Monte Carlo simulations and steady-state pharmacokinetic data from hospitalized patients. Ann Pharmacother. 2009;43(11):1747-1754.
- Societe Francaise de Pharmacologie et de Therapeutique and Societe Francaise d’Anesthesie et de Reanimation. Recommandations de Pratiques Professionnelles: optimisation du traitement par beta-lactamines chez le patient de soins critiques. 2018; published in English as Guilhaumou R et al, Crit Care. 2019;23:104. Recommendation R2.2.
- ZOSYN (piperacillin and tazobactam) for injection. US prescribing information, Clinical Pharmacology. Source for about 30% binding of both components and a half-life of 0.7 to 1.2 hours.
- MERREM I.V. (meropenem for injection). US prescribing information, NDA 50-706/S-022, Clinical Pharmacology. Source for about 2% binding and a half-life of about 1 hour.
- Mouton JW, Muller AE, Canton R, Giske CG, Kahlmeter G, Turnidge J. MIC-based dose adjustment: facts and fables. J Antimicrob Chemother. 2018;73(3):564-568. Source for the log2 variability figures, the ISO 20776-2 criterion and the stated conclusion that individual MIC-based dose adjustment is not justified.
Not medical advice. For healthcare professionals and education. Reference intervals vary by laboratory and assay — always use your own laboratory's. Never base a dose or a treatment decision on this page alone. Full disclaimer at calcengines.com/disclaimer/