The simplest pharmacokinetic (PK) model treats the entire body as one well-mixed compartment. Adjust the dose, volume of distribution, elimination and absorption rate constants, and the simulator updates the plasma concentration–time profile, half-life, clearance, AUC, Cmax and Tmax in real time, making the difference between IV bolus and oral dosing immediately obvious.
Parameters
Route of administration
IV bolus: instantaneous injection. Oral: absorbed from the gut.
Dose D
mg
Volume of distribution V_d
L
Apparent volume the drug would occupy at the measured plasma concentration
Time to peak for oral dosing. As k_a → k_e the formula needs l'Hôpital's rule (implementation uses a small-ε limit to stay finite).
What is one-compartment pharmacokinetics?
🙋
Professor, when you swallow a pill, what actually happens to the drug inside the body? Can you scan it like an X-ray and say "3 mg is sitting in the liver"?
🎓
Usually we just draw blood and measure the concentration. But the body has the brain, muscles, fat — modelling all those organs separately gets unsolvable fast. So pharmacologists said, "let's pretend the whole body is one big beaker." That's the one-compartment model. The drug instantly mixes into a 'volume of distribution' V_d, and then leaks out at first-order rate k_e. Beautifully simple.
🙋
But the body isn't simple at all. Can you really decide drug doses from such a crude picture?
🎓
Great pushback! Surprisingly, yes, for drugs that equilibrate quickly between tissues — caffeine, ethanol, most antibiotics. The diagnostic is to plot log(C) vs t: if it's a straight line, one compartment is fine. Anesthetics that pool in brain, or diazepam that sinks into fat, need two or three compartments. But roughly 80% of practical PK work runs on the one-compartment model precisely because it gives you half-life and clearance in one line of arithmetic.
🙋
When I flip the route selector from IV to Oral, the curve totally changes — IV starts at the peak and decays, but oral makes a hill. Why?
🎓
That's the heart of PK. With IV the drug enters the bloodstream instantly, so at t = 0 the concentration is already at its peak D/V_d. From then on it just decays at rate k_e. Oral has to climb out of the gut into the blood first, so initially absorption exceeds elimination and concentration rises. At some time Tmax the two rates balance — that's the peak — and after that elimination dominates and the curve falls. For k_a = 1.0 and k_e = 0.1, Tmax = ln(10)/0.9 ≈ 2.6 hours.
🙋
What exactly is bioavailability F? It only appears in the oral case.
🎓
F is the fraction of an oral dose that reaches the systemic circulation intact. Some drug dissolves badly, some doesn't cross the gut wall, and what does cross often hits the liver first and gets chewed up — that's the first-pass effect. Propranolol, a beta-blocker, has F ≈ 30%, so an oral dose has to be three times the IV dose for the same effect. Drugs with F > 90% can be swapped one-to-one. Forgetting F is one of the most dangerous mistakes in dosing calculations.
🙋
AUC, the area under the curve — that sounds like a statistics term. Why is it so central to drug dosing?
🎓
Because AUC is the total time-integrated exposure: how many mg·h/L of drug the body has seen. The formula is just AUC = D/CL, proportional to dose and inversely proportional to clearance. Carboplatin is dosed to AUC = 5 using the Calvert equation. Generic drug approval requires the generic AUC and Cmax to lie within 80–125% of the brand-name's value. And when two patients on the same dose end up with twofold-different AUCs, the culprit is almost always individual variation in CL.
Frequently asked questions
The one-compartment model treats the whole body as a single, well-mixed container. The administered drug is assumed to distribute instantly into a volume V_d and then to decline by first-order elimination with rate constant k_e. For IV bolus this gives C(t) = D/V_d · exp(-k_e·t), producing a straight line on a semi-log plot of concentration vs time. Real bodies have heterogeneous tissues (brain, fat, muscle), but for drugs whose inter-tissue equilibration is fast — caffeine, ethanol, many antibiotics — one compartment is a very good approximation and gives clean numbers for half-life and clearance.
Half-life is t1/2 = ln2 / k_e and clearance is CL = k_e · V_d, so t1/2 = ln2 · V_d / CL. Half-life therefore scales with V_d and inversely with CL. For V_d=30L and k_e=0.1/hr you get t1/2 ≈ 6.9 hr and CL = 3.0 L/hr. In renal impairment CL drops and, for the same V_d, half-life is prolonged — so dosing interval is lengthened or the dose is cut. Clearance is best read as "the blood volume cleared of drug per unit time" and represents the sum of hepatic metabolism and renal excretion.
Oral dosing follows a double-exponential: drug enters the central compartment with rate k_a and leaves with k_e, giving C(t) = F·D·k_a / [V_d·(k_a - k_e)] · (exp(-k_e·t) - exp(-k_a·t)). Setting dC/dt = 0 yields Tmax = ln(k_a/k_e) / (k_a - k_e). For k_a = 1.0 and k_e = 0.1 this is ln(10)/0.9 ≈ 2.56 hr. F is the oral bioavailability and absorbs the loss to incomplete absorption and the first-pass effect. Drugs with low F such as propranolol (F ≈ 30%) require substantially larger oral than IV doses to achieve the same exposure.
AUC0–∞, the integral of the concentration–time curve, is the total systemic exposure and is the key predictor of efficacy and toxicity. In the one-compartment model AUC = D/(k_e·V_d) = D/CL, so AUC is proportional to dose and inversely proportional to clearance. For D=500 mg, k_e=0.1/hr and V_d=30 L you get AUC ≈ 166.7 mg·h/L. For oral dosing AUC = F·D/CL, which lets you compare IV and oral curves to estimate bioavailability. Narrow-therapeutic-index drugs such as carboplatin are dosed to a target AUC (e.g. AUC = 5) instead of milligrams.
Real-world applications
Antibiotic dosing and therapeutic drug monitoring (TDM): Vancomycin and aminoglycosides have narrow margins between therapeutic and toxic concentrations, so plasma levels are measured and dosing adjusted on the fly. Hospital pharmacists fit a one-compartment model to each patient's V_d and k_e and pick the next dose and interval so that AUC sits in the target window (for vancomycin, AUC/MIC = 400–600). Renal-function estimates (Cockcroft-Gault) and Bayesian fitting feed k_e back into the same loop.
AUC-based cancer chemotherapy (Calvert formula): Carboplatin is dosed to an AUC target of 5–7 mg·min/mL. The Calvert equation Dose = AUC × (GFR + 25) is exactly the one-compartment AUC = D/CL rewritten in terms of renal function. The 1980s discovery that dosing by GFR — not by body surface area — gives much more reproducible hematological toxicity made this the standard approach for platinum drugs.
Bioequivalence studies for generics: Generic drug approval requires AUC and Cmax to fall inside 80–125% of the reference brand (90% CI). 24–36 healthy volunteers swallow both products, blood is drawn at 15 or so time points, and AUC is extracted by either a one-compartment fit or non-compartmental analysis. A difference in F large enough to shift AUC outside the window means the generic fails registration.
First-in-human Phase I trials: When a new drug is first given to humans, doses are escalated cautiously and plasma sampling provides the first-ever human estimates of V_d, k_e, CL and F. These are compared with allometric scaling from animal studies and used to choose Phase II doses. If a single compartment cannot fit, the team escalates to two- or three-compartment or full population PK (NONMEM) analyses.
Common misconceptions and pitfalls
The biggest trap is to confuse the volume of distribution V_d with an actual fluid compartment. V_d is just "the volume that, multiplied by the measured plasma concentration, gives the dose in the body". Total body water is about 42 L, but reported V_d values range from 5 L for warfarin (heavily protein-bound) to 7,000 L for chloroquine (deeply tissue-bound) — a hundred-fold span. Drugs with V_d larger than body weight are not "diluted in plasma" at all; they are sequestered in tissues, so detoxification by haemodialysis barely budges them. The 1–200 L slider range here is set to cover most commonly used drugs.
Another mistake is the leap from "long half-life equals once-daily dosing". A 24-hour half-life makes once-daily steady state plausible, but how acceptable the Cmax/Cmin ratio is depends entirely on the therapeutic window. Narrow-window drugs may still need two or three daily doses despite a long half-life; conversely, a slow-release formulation can squeeze a short-half-life drug into once-daily use. Use the half-life to estimate time to steady state (~4–5 × t1/2) and washout after stopping, but make the interval decision from window, compliance and formulation together.
Finally, do not assume first-order kinetics always hold. This model assumes k_e is independent of concentration, but ethanol and phenytoin show enzyme saturation and follow Michaelis-Menten kinetics, blending zero- and first-order behaviour. Ethanol disappears at a roughly constant 7 g/hr regardless of concentration; a small phenytoin dose increase near the saturation point can produce a runaway concentration rise. This simulator is an educational, first-order, single-compartment tool — it cannot guide clinical decisions in saturation regimes.
How to Use
Enter the administered dose in mg (typical range 100–1000 mg for oral drugs)
Set the volume of distribution (Vd) in L, representing total body water distribution (e.g., 50 L for a 70 kg adult)
Input the elimination rate constant (ke) in h⁻¹, derived from clearance or half-life data
For oral dosing, specify the absorption rate constant (ka) in h⁻¹ to model GI transit and membrane permeability
The simulator calculates half-life, clearance, peak concentration, time-to-peak, area under the curve, and residual concentration at 12 hours
Worked Example
Consider amoxicillin: dose = 500 mg, Vd = 18 L, ke = 0.173 h⁻¹ (t₁/₂ = 4 h), ka = 1.5 h⁻¹. The simulator returns C_max = 18.2 mg/L at T_max = 1.8 h, CL = 3.1 L/h, AUC₀₋∞ = 161 mg·h/L, and concentration at 12 h = 2.1 mg/L. These values align with therapeutic drug monitoring ranges used in clinical pharmacology.
Practical Notes
Renal impairment increases ke values; dialysis patients (GFR <15 mL/min) may require dose reductions of 50–75%
Hepatic metabolism affects ke significantly—cirrhotic patients exhibit prolonged half-lives (e.g., warfarin t₁/₂ doubles from 40 to 80 h)
Food interactions alter ka; fatty meals delay peak concentration by 1–3 hours but rarely affect total AUC for high-solubility drugs
Use steady-state calculations (dose/CL × τ where τ = dosing interval) for repeated dosing schedules in pediatric or obese populations