Compartmental and physiologically based models of drug absorption, distribution, metabolism and excretion, used to translate in vitro data and animal studies into human dose.
Dose selection, first-in-human predictions, drug-drug interaction assessment and regulatory submissions all use PK/PBPK models; their predictive error limits how many candidates fail in the clinic for exposure reasons.
Mathematical models of how a drug travels through the body and how fast it is removed.
1Dose enters the body
2Spreads to tissues
3Liver and kidney remove it
4Clearance sets exposure
5Exposure sets the dose
One-compartment model. If the body is a single well-mixed volume V and the drug is removed at a rate proportional to its concentration with constant k, then after an intravenous dose D the concentration is C(t)=. Clearance is and the total exposure (area under the concentration curve) is , so clearance sets the dose needed for a target exposure.
Go deeper
The full technical text.
What it is
Pharmacokinetics (PK) describes how drug concentration C(t) in blood or tissue evolves after dosing. The one-compartment model with first-order elimination is C(t)=V with clearance ; exposure (AUC) is for intravenous dosing. Clearance and volume of distribution are the two numbers that drive dose and dosing interval.
Wood et al. show the majority of predictions fall outside 2-fold for both microsomes and hepatocytes.
Discussion
(
D
/
V
)
e−kt
CL=kV
AUC=D/CL
Population models. Nonlinear mixed-effects models (NONMEM and others) estimate typical values and between-patient variability, and how covariates such as weight or kidney function shift them.
PBPK. Physiologically based models give each organ a volume and blood flow and predict tissue distribution from the molecule's properties. For the liver, the well-stirred model gives hepatic clearance CLH=Q+fuCLintQfuCLint, where Q is liver blood flow, fu the fraction of drug not bound to protein and CLint the enzymes' intrinsic capacity.
IVIVE. In vitro-in vivo extrapolation measures CLint in liver microsomes or hepatocytes and scales it up. Systematic under-prediction of 3 to 10 fold is common, and most predictions miss by more than a factor of two. Transporters, non-liver metabolism and enzymes such as aldehyde oxidase (which differs strongly between species) are common causes.
Machine learning. Models trained on measured clearances of known drugs typically report 40 to 60 percent of predictions within two-fold, mostly in retrospective tests.
Try it. Simulate the one-compartment model in a spreadsheet for two clearances differing by a factor of two and compare the exposure after a fixed dose; this shows concretely why a two-fold error in predicted clearance is the usual yardstick.
D
e−kt
CL=kV
Dose/CL
The core machinery
Compartmental and population PK. Mamillary compartment models, nonlinear mixed-effects modelling (NONMEM, Monolix) with inter-individual variability and covariates; population PK/PD links exposure to response.
PBPK. Organs are compartments with real volumes and blood flows, connected by the circulation; tissue partitioning is predicted from physicochemical properties (Rodgers-Rowland), and metabolism is scaled from in vitro assays to the whole liver. The well-stirred liver model gives CLH=QH+fuCLintQHfuCLint for hepatic blood flow QH, unbound fraction fu and intrinsic clearance CLint.
In vitro-in vivo extrapolation (IVIVE). Intrinsic clearance from microsomes or hepatocytes is scaled by cell/enzyme content per gram liver; transporters and extrahepatic metabolism add steps. Systematic under-prediction by 3- to 10-fold is common, forcing empirical scaling factors, and reviews report most predictions falling outside 2-fold.
Biologics and special cases. Target-mediated drug disposition for antibodies, FcRn recycling, nanoparticles, and paediatric or organ-impairment scaling need different model structures.
Machine learning. Models trained on measured human or animal PK from structure predict clearance, volume and half-life; reported 2-fold accuracy of structure-only models is typically about 40-60 percent, validated mostly retrospectively.
Techniques to master
ODE modelling, nonlinear mixed-effects estimation, identifiability and sensitivity analysis, allometric scaling, IVIVE assumptions, model qualification and the regulatory (FDA/EMA) framework for PBPK.
Where it bites
The open problem is to predict human clearance for new chemical matter before synthesis, within 2-fold for most compounds, reliably enough to remove an assay stage, and to say honestly when it cannot.
What to read before Pharmacokinetic and PBPK modelling (left), and what builds on it: entries that depend on it and the open problems it hosts (right). Every box links to its page.