One-compartment PK basics — learn what CL, Vd, K, and t½ mean through a live model.
Drug In (Infusion)
Body (Vd)50 L
Drug Out (CL)
Parameters
Clearance (CL)5 L/hr
Volume (Vd)50 L
Dose1000 mg
Infusion Time1 hr
K (elim. rate)
0.100 hr⁻¹
Half-Life
6.93 hr
Cmax
-- mg/L
AUC₀₋∞
-- mg·hr/L
Try it: Drag the Vd slider up — the "bucket" gets bigger, so Cmax drops. Now drag CL up — the "drain" opens wider, so the curve falls faster.
Key equations: K = CL ÷ Vd | t½ = 0.693 ÷ K | AUC = Dose ÷ CL
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Build a Patient
See how patient demographics drive PK parameters through covariate relationships.
Patient Demographics
Computed
Dosing
CL
-- L/hr
Vd
-- L
t½
-- hr
Cmax,SS
-- mg/L
Cmin,SS
-- mg/L
AUC₂₄,SS
-- mg·hr/L
Try it: Change weight from 70 to 120 kg — watch Vd increase and Cmax decrease. This is why obese patients may need higher doses. Use "Snapshot" to compare two patients side-by-side.
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Why Population PK?
See interindividual variability (IIV) come alive — this is why one-size-fits-all dosing fails.
Simulated Patients
Interindividual Variability (IIV)
ω CL (CV%)30%
ω Vd (CV%)25%
Typical Patient (Cefepime)
Dose2000 mg
Frequency8 hr
Infusion Time0.5 hr
MIC8 mg/L
Patients Above Target
--
Patients Below Target
--
fT>MIC Target
100%
Key insight: Set both ω to 0% — everyone gets the same curve. This is what traditional PK assumes. Now increase ω CL to 40% — watch the spread. This is real life.
Clinical implication:With this variability, some patients are underdosed and some overdosed — population PK helps us predict who needs what.
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How Covariates Reduce Uncertainty
Every piece of patient data you collect narrows the prediction — toggle covariates to see uncertainty shrink.
Patient (Vancomycin)
Dosing
Covariate Switches
ON = use patient's actual value | OFF = use population mean (adds uncertainty)
Weight: population mean
CrCL: population mean
Age: population mean
Albumin: population mean
This is the power of popPK: every piece of patient data you collect reduces your uncertainty about what the drug is doing. Toggle each covariate ON and watch the prediction band narrow.
5
One-Compartment vs. Two-Compartment
Understand when and why distribution matters — watch the alpha phase appear.
Drug In
Central (V1)15 L
Q
5 L/hr
Peripheral (V2)15 L
Drug Out (CL)
Compartment Parameters
V1 (Central)15 L
V2 (Peripheral)15 L
Q (Intercomp. CL)5 L/hr
CL (Elimination)5 L/hr
Dosing
Dose1000 mg
Infusion Time0.5 hr
α (distribution)
-- hr⁻¹
β (elimination)
-- hr⁻¹
t½α
-- hr
t½β
-- hr
Overlay both on one chart
One-Compartment
Two-Compartment
Distribution phase (α): The sharp initial drop — drug leaving blood and entering tissues. Drugs with large V2 or fast Q show a pronounced distribution phase.
Clinical examples: Vancomycin, aminoglycosides, and daptomycin all require two-compartment models for accurate predictions.
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Accumulation to Steady State
Watch repeated doses stack up — see why it takes 4-5 half-lives to reach steady state.
Parameters
Half-Life6 hr
Dose1000 mg
Frequency (τ)8 hr
Infusion Time0.5 hr
K (elim. rate)
0.116 hr⁻¹
CL
5.78 L/hr
SS Cmax
-- mg/L
SS Cmin
-- mg/L
Accumulation Progress
Dose0 of 0
Current Peak--
Current Trough--
Key insight: Time to steady state depends ONLY on half-life, not on dose or frequency. It always takes ~4-5 half-lives regardless of the regimen.
Rule of thumb: ~50% of SS after 1 t½, 75% after 2, 87.5% after 3, 93.75% after 4, ~97% after 5. This is why we say "4-5 half-lives to steady state."
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The Loading Dose
Accumulation is slow — it takes 4–5 half-lives to reach target. A loading dose gets there on the first dose. See why it depends on volume, not clearance.
Target & Drug
Target concentration (Css)20 mg/L
Volume of distribution (Vd)49 L
Clearance (CL)4 L/hr
Maintenance Regimen
Interval (τ)12 hr
Infusion Time1.5 hr
Loading Dose = Css × Vd
-- mg
Maintenance = Css × CL × τ
-- mg
Half-Life
-- hr
Time to 90% SS (no load)
-- hr
Show the same regimen without a loading dose
Read it: the loaded curve hits the target on dose 1; the un-loaded curve crawls up over several half-lives to the same place.
The key idea: drag Clearance — the loading dose doesn’t move (it’s set by Vd), but the maintenance dose does. Then drag Vd — now the loading dose changes. Loading dose comes from the size of the tank; maintenance comes from how fast it drains.
Why it matters: try the Vanco (renal impairment) preset — with a ~34 h half-life, skipping the load means days of underdosing. And because critical illness expands Vd, loading doses are weight-based (vancomycin 25–30 mg/kg).
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Probability of Target Attainment
The bedside question made quantitative: across a whole population of patients, what fraction hit the PK/PD target at each MIC? This is how dosing regimens are actually validated.
Regimen
Dose2000 mg
Frequency (τ)8 hr
Infusion Time0.5 hr
Patient & Variability
CrCL (renal function)100 mL/min
ω CL (CV%)30%
PK/PD Target (fT>MIC)
Default is 100% fT>MIC, the critically-ill standard (SFPT/SFAR, Guilhaumou 2019). Toggle to the lower textbook targets — Meropenem 40%, Pip/Tazo 50%, Cefepime 60% — to see how target choice shifts the PTA curve.
Simulated Patients
PK/PD Breakpoint (PTA ≥ 90%)
--
Typical CL (from CrCL)
--
Read it like this: each point is the % of a simulated population reaching the target at that MIC. The highest MIC still at or above the 90% line is the regimen's PK/PD breakpoint.
Try it: keep the dose fixed and drag Infusion Time from 0.5 h to 4 h — watch the whole PTA curve shift right (a higher breakpoint) with no extra drug. That is the entire case for extended and continuous β-lactam infusions. Then drop CrCL to 30 (renal impairment) and see the curve climb as the drug lingers.
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Bayesian Estimation from Drug Levels
Module 4 showed covariates shrink uncertainty. A measured drug level shrinks it further. Bayesian estimation blends the population prior with the patient’s own levels to individualize the curve — the engine behind modern AUC-guided vancomycin dosing.
Population Prior (Vancomycin)
CrCL → typical CL90 mL/min
ω CL (CV%)30%
ω Vd (CV%)20%
Regimen
Dose1000 mg
Interval (τ)12 hr
Measured Levels
Assay / model error (σ)15%
Level 1 — concentration18 mg/L
Level 1 — time after dose11.5 hr
Add a second level (peak) to resolve Vd
Level 2 — concentration30 mg/L
Level 2 — time after dose2 hr
Clearance (pop → indiv)
--
Vd (pop → indiv)
--
AUC₂₄ (individualized)
-- mg·hr/L
Half-Life (indiv)
-- hr
Read it: the blue posterior passes near the red measured level, not exactly through it — pulled toward the data but held back by the population prior.
The trust dials: raise ω (more population variability) and the estimate leans on the level; raise σ (noisier assay) and it leans back on the population. At the extremes it becomes “believe the data” vs “believe the textbook.”
One level vs two: a single trough mostly individualizes clearance (and AUC). Toggle on a second (peak) level and the fit can resolve Vd too — watch the posterior snap onto both points. This is why AUC-guided vancomycin uses Bayesian software rather than raw peak-and-trough kinetics.
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Test Your Knowledge
Build graph-reading and PK estimation skills with interactive questions.