Time Above MIC Calculator (fT>MIC)
Time Above MIC Calculator (fT>MIC)
The fraction of the dosing interval during which free drug stays above the MIC — the target that belongs to the beta-lactams, computed in closed form from the peak, the half-life and the interval, with what one doubling dilution of MIC does to it.
fT>MIC for an intermittent regimen
Peak + half-life + MICfree peak 40 mg/L, MIC 4 mg/L, half-life 1.0 h, interval 8 h
The closed form, and where it comes from
- the derivation
- in one compartment at steady state the concentration after an instantaneous dose is C(t) = Cmax e^(-ke t). C(t) > MIC when e^(-ke t) > MIC/Cmax, that is when -ke t > ln(MIC/Cmax), that is when t < ln(Cmax/MIC) / ke. Divide by the interval τ for the fraction, and clamp to [0, 1]
- the half-life form
- substituting ke = ln 2 / t½ gives T>MIC = t½ × log₂(Cmax / MIC). The time above the MIC is the half-life multiplied by the number of DOUBLINGS between the peak and the MIC — so one doubling dilution of MIC is worth exactly one half-life of T>MIC, whatever the drug
- Cmax
- the steady-state peak of FREE drug. A target expressed in free terms and a total-drug measurement are not comparable, and for a 95%-bound agent they differ twentyfold
- the model assumptions
- one compartment, first-order elimination, instantaneous input, steady state. Each one fails somewhere: a real infusion is not instantaneous (use the extended versus intermittent infusion calculator), distribution is rarely one-compartment in the first hour, and in critical illness the volume of distribution and the clearance both move, often day to day
Worked example
free peak 40 mg/L, MIC 4 mg/L, half-life 1.0 h, interval 8 h
ke = ln 2 / 1.0 = 0.6931 per hour
ln(40 / 4) / 0.6931 = 2.3026 / 0.6931 = 3.32 hours above the MIC — which is also 1.0 × log₂(10) = 3.32, one half-life per doubling
3.32 / 8 = 41.5% of the dosing interval
The free trough is 40 × e^(-0.6931 × 8) = 0.156 mg/L, well below the MIC, so the concentration spends the remaining 4.7 hours of each interval under it
Now move the MIC one doubling dilution: at 2 mg/L the answer is 54.0%, at 8 mg/L it is 29.0%. A 25-percentage-point spread, from a measurement whose accepted reproducibility is exactly that one dilution
Halve the interval to 4 hours and the answer becomes 83.0%; the dose per interval would have to halve to keep the daily total, which lowers the peak and gives back part of the gain
Published %fT>MIC targets for the beta-lactams
| Class | Stasis | 1-2 log10 kill | Model and source |
|---|---|---|---|
| Penicillins | not stated in the source read | 50-60% | Neutropenic murine models; Berry and Kuti 2022, attributing Turnidge 1998 |
| Cephalosporins | 30-40% | 60-70% | Neutropenic murine thigh; Berry and Kuti 2022, attributing Craig 1998 |
| Carbapenems | about 20% (doripenem) | about 40% | Neutropenic murine thigh and lung; Berry and Kuti 2022 |
| Critically ill, any beta-lactam | — | free concentration 4-8 × MIC for 100% of the interval | SFPT/SFAR 2018 recommendation R2.2, as expert suggestion |
What the human studies found, which is less tidy
| Study | What it tested | Result |
|---|---|---|
| DALI (reported in Berry and Kuti 2022) | 50% against 100% fT>MIC in critically ill patients | Patients who did not reach at least 50% fT>MIC were 32% less likely to have a positive clinical outcome; the ROC analysis showed no clear difference between the 50% and 100% targets |
| EXPAT (reported in Berry and Kuti 2022) | 100% fT>MIC and 100% fT>4×MIC | 63.3% reached the first and 36.7% the second; neither was significantly associated with 30-day survival |
| Ceftaroline and cefiderocol phase 3 (reported in Berry and Kuti 2022) | Exposure against study endpoints | No relationship with any endpoint, even at 100% fT>4×MIC |
| BLING III (Dulhunty 2024) | Continuous against intermittent infusion, 7,031 patients | 90-day mortality 24.9% against 26.8%; unadjusted odds ratio 0.91 (0.81-1.01, P = 0.08), prespecified adjusted 0.89 (0.79-0.99, P = 0.04) |
One half-life per doubling, and why that is the whole story
The beta-lactams are time-dependent: raising the peak above the MIC buys very little extra killing, while keeping the free concentration above the MIC for longer buys a great deal. The index that tracks that is the fraction of the dosing interval during which free drug exceeds the MIC, written %fT>MIC, and it is one of the few PK/PD quantities with an exact closed-form solution. In a one-compartment model with first-order elimination the concentration falls as Cmax e^(-ke t), so the time it spends above a threshold is ln(Cmax/MIC) divided by the elimination rate constant — and dividing by the dosing interval turns the time into a fraction.
Rewriting ke as ln 2 over the half-life gives the form worth remembering: the time above the MIC equals the half-life multiplied by the number of doublings between the peak and the MIC. One doubling of the MIC costs exactly one half-life of time above it. For piperacillin, with a half-life near one hour, each doubling dilution of MIC costs an hour out of every dosing interval; for ceftriaxone at six hours it costs six. That single identity explains why carbapenem and penicillin regimens have to be given frequently or infused slowly while ceftriaxone can be given once a day, and it explains why the MIC’s own measurement resolution matters so much here. Susceptibility testing works in doubling dilutions, so a reported MIC of 1 mg/L means growth was inhibited at 1 mg/L and not at 0.5 mg/L — the true value lies somewhere in that bracket, and inter-laboratory reproducibility of one doubling dilution either way is the accepted standard. Any ratio with an MIC in it therefore carries at least a twofold uncertainty, which is larger than the precision in the rest of the calculation.
Three assumptions carry the arithmetic, and all three are worth stating because they fail in exactly the patients who are hardest to dose. The input is treated as instantaneous, which is wrong for an infusion of any length and is the subject of its own page here. Distribution is treated as one-compartment, which is wrong in the first hour after a dose and is why a peak must be drawn after distribution is complete. And steady state is assumed, which takes four to five half-lives — a level drawn earlier reflects accumulation still in progress. In critical illness the volume of distribution expands and renal clearance may be augmented or collapsed, sometimes both within a week, so the half-life entered today may not be the half-life tomorrow.
What this page deliberately does not do is read across from the answer to a decision. 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 maintenance dose calculator turns a clearance and a target concentration into a dose per interval, and the Cockcroft-Gault creatinine clearance calculator gives the clearance most drug labels specify. This page answers only the question they do not: given the exposure you have and the MIC the laboratory reported, what fraction of the interval is the organism actually seeing drug?
Frequently asked questions
What is fT>MIC?
The fraction of a dosing interval during which the concentration of FREE (unbound) drug stays above the organism’s MIC, usually written as a percentage. It is the pharmacodynamic index that predicts the activity of the beta-lactams, which are time-dependent killers: concentrations far above the MIC add little, duration above it adds much.
How is the time above the MIC calculated?
For an intermittent bolus in one compartment with first-order elimination at steady state, T>MIC = ln(Cmax/MIC) / ke, where ke is the elimination rate constant. Substituting ke = ln 2 / half-life gives the more memorable T>MIC = half-life × log₂(Cmax/MIC) — the half-life times the number of doublings between the peak and the MIC. The fraction is that time divided by the dosing interval.
What percentage of the interval is the target?
It depends on the class and on the endpoint. In neutropenic murine models, reported by Berry and Kuti in 2022: cephalosporins need 30 to 40% for stasis and 60 to 70% for a 1 to 2 log10 kill, penicillins 50 to 60% for maximal effect, carbapenems about 40%.
Should I use the total or the free concentration?
The free concentration. Every published fT>MIC target is a free-drug target, and most assays report total drug. For meropenem, at about 2% bound, the difference is negligible; for ceftriaxone, at 95% bound falling to 85% at high concentrations, the total concentration is between seven and twenty times the free one. Mixing a total measurement with a free target is one of the real errors in this area.
Why does one doubling dilution of MIC change the answer so much?
Because the relationship is logarithmic in Cmax/MIC and linear in the half-life: one doubling of the MIC removes exactly one half-life of time above it. At the page’s defaults — a half-life of 1 hour and an 8-hour interval — that is 12.5 percentage points per dilution, so the answer moves from 54.0% to 29.0% across the one-dilution bracket the measurement itself carries.
Does this page tell me whether the organism is susceptible?
No. This page cannot say whether an organism is susceptible: that is a laboratory interpretation against a versioned breakpoint table, and the laboratory that issued the report has already made it.
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.
- 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.
- 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.
- 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.
- European Committee on Antimicrobial Susceptibility Testing. Breakpoint tables for interpretation of MICs and zone diameters, version 16.1, 2026, stated valid 24 June to 31 December 2026. https://www.eucast.org. Cited rather than reproduced.
- Ceftriaxone for injection, USP. US prescribing information, Clinical Pharmacology. Source for 95% binding below 25 mcg/mL falling to 85% at 300 mcg/mL, and a half-life of 5.8 to 8.7 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.
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/