One-Compartment IV Infusion Model Calculator
Model plasma drug concentration during and after a continuous IV infusion, with automatic detection of the infusion versus post-infusion phase.
🫗 What is the One-Compartment IV Infusion Model?
The one-compartment IV infusion model describes how plasma drug concentration rises during a continuous intravenous infusion, approaches a theoretical steady-state level, and then declines once the infusion stops. It extends the basic one-compartment framework by modeling drug entering the body continuously at a constant rate (R0) rather than all at once, giving the equation C(t) = Css x (1 - e^(-ke t)) during infusion.
Critical care and hospital pharmacists use this model to predict how quickly a continuous infusion (common for antibiotics, sedatives, and vasopressors) approaches its target concentration, and to time when the infusion has run long enough to reach clinically meaningful levels. Anesthesiologists use the post-infusion decline phase to estimate how quickly a sedative will wear off after stopping a continuous drip. Pharmacokinetics students use it as the natural second model after the IV bolus, since it introduces the concept of a rate-in versus rate-out balance producing a genuine steady state.
A common misconception is that stopping an infusion causes concentration to drop instantly. It does not, concentration declines by the same first-order exponential process as any other elimination, just starting from whatever level the infusion had actually reached, which may be well below the theoretical steady-state value if the infusion ran for only a short time.
This calculator automatically detects whether your chosen evaluation time falls during or after the infusion, applies the correct equation for that phase, and plots the complete rise-then-fall concentration profile.
📐 Formula
📖 How to Use This Calculator
Steps
💡 Example Calculations
Example 1 — Concentration at the End of Infusion
R0 = 100 mg/hr, Vd = 40 L, ke = 0.2/hr, Tinf = 4 hr, evaluate at t = 4 hr
Example 2 — Concentration After Infusion Stops
R0 = 50 mg/hr, Vd = 20 L, ke = 0.1/hr, Tinf = 6 hr, evaluate at t = 10 hr
Example 3 — Mid-Infusion Concentration
R0 = 200 mg/hr, Vd = 50 L, ke = 0.15/hr, Tinf = 8 hr, evaluate at t = 3 hr
❓ Frequently Asked Questions
🔗 Related Calculators
What is the formula for concentration during a continuous IV infusion?
During infusion, C(t) = Css x (1 - e^(-ke t)), where Css = R0 / (Vd x ke) is the theoretical steady-state concentration, R0 is the infusion rate, Vd is volume of distribution, and ke is the elimination rate constant.
What happens to concentration after the infusion stops?
Once the infusion ends, the concentration at that moment (call it C at Tinf) simply declines by standard first-order elimination: C(t) = C(Tinf) x e^(-ke(t - Tinf)) for any time t after the infusion stopped, the same exponential decay as an IV bolus starting from that concentration.
What is steady-state concentration (Css)?
Css = R0 / (Vd x ke) is the concentration an infusion would eventually plateau at if continued indefinitely, since the rate of drug entering the body (R0) exactly balances the rate being eliminated once concentration is high enough. It's an asymptote, not necessarily the concentration when a finite-duration infusion actually ends.
How long does it take to reach steady state during an infusion?
By half-life multiples: about 50% of Css after 1 half-life, 75% after 2, 87.5% after 3, and roughly 90% after 3.3 half-lives, 97% after 5 half-lives. This means steady state is governed entirely by the drug's half-life, not by the infusion rate itself.
Why does the concentration curve rise then fall in this model?
While the infusion runs, drug enters faster than it is initially eliminated, so concentration rises (approaching but never quite reaching Css). Once the infusion stops, no more drug enters, so elimination alone takes over and concentration declines exponentially from whatever level it had reached.
Can I use this model if the infusion is stopped before reaching steady state?
Yes, that's exactly what the 'after infusion' phase calculates, it takes the actual concentration reached at the moment the infusion stopped (which may be well below Css if it ran only briefly) and applies standard exponential decline from there.
How does infusion rate affect steady-state concentration?
Css is directly proportional to infusion rate: doubling R0 exactly doubles Css, since Css = R0 / (Vd x ke) and Vd and ke are properties of the drug and patient, not the infusion itself. This makes infusion rate the primary lever for targeting a specific steady-state level.
What is the difference between this model and the IV bolus model?
The IV bolus model assumes the entire dose enters instantly, producing an immediate peak (C0) followed by pure exponential decline. The infusion model spreads drug entry over time, producing a gradual rise toward Css during the infusion, followed by exponential decline only after the infusion stops.
What units should I use for infusion rate?
Enter infusion rate in milligrams per hour (mg/hr), volume of distribution in liters, and the elimination rate constant in per hour, this combination gives concentration directly in mg/L. Infusion duration and evaluation time should both be in hours.
Does a loading dose change this calculator's results?
No, this calculator models the infusion alone, starting from zero drug in the body. A loading dose given at the start of an infusion would add its own IV bolus concentration contribution on top of what this calculator shows, use the One-Compartment IV Bolus Model Calculator alongside this one to combine both effects manually.