Pharmacokinetic (PK) Analysis — Non-Compartmental Analysis

Turn a concentration-vs-time profile after a dose into the standard PK parameters, and compute bioavailability from IV + oral data. Non-compartmental analysis (NCA) is the model-independent workhorse used for most PK reporting.

When to use this

• You have measured plasma/serum (or other matrix) drug concentrations at known times after a dose.
• You need Cmax/Tmax/AUC/half-life/clearance/Vd, or absolute bioavailability F.
• Comparing exposure (AUC, Cmax) between formulations, doses, or routes.

This is measured-data PK. For predicting ADMET properties from a chemical structure, use tooluniverse-admet-prediction.

Step 1 — Prepare the concentration-time data

Issue	What to do
Units — be consistent	One time unit (h), one concentration unit (mg/L or ng/mL), one dose unit (mg). Pass them as time_unit/conc_unit/dose_unit. CL and Vd come back in derived units (e.g. L/h, L).
Route matters	Set route to iv or po/oral. CL and Vd are only directly interpretable for IV data; from oral data they are apparent (CL/F, Vd/F) because absorption is incomplete.
Include t=0	For IV bolus include the t=0 (back-extrapolated) point; for oral the pre-dose value is usually 0.
BLQ (below limit of quantification)	Leading BLQs before the first measurable → treat as 0; BLQs in the terminal tail → drop them (don't set to 0, it corrupts the terminal slope).
Sampling design	You need enough late points to define the terminal phase (≥3 points clearly in the log-linear decline) or the half-life and AUC0-∞ are unreliable.
Single vs multiple dose	NCA here assumes a single dose. For steady-state, analyze one dosing interval (AUC0-τ) and say so.

Step 2 — Run NCA

tu run NCA_compute_parameters '{
  "times":[0,0.5,1,2,4,8,12,24],
  "concentrations":[0,2.5,4.8,6.1,4.2,2.1,1.0,0.2],
  "dose":100, "route":"iv",
  "dose_unit":"mg", "conc_unit":"mg/L", "time_unit":"h"}'

Returns Cmax, Tmax, Clast, Tlast, AUC0_last, AUC0-inf, AUC_extrapolation_pct, lambda_z, t_half, r_squared_terminal_fit, clearance_CL, volume_distribution_Vd, MRT_iv, with a units block. AUC uses the FDA/EMA linear-up / log-down trapezoidal method.

For a CSV profile (with BLQ handling), scripts/nca_from_csv.py computes the same parameters locally.

Other tools:

• NCA_fit_one_compartment — fit a 1-compartment model (k, V, CL) when you want a parametric model instead of NCA.
• NCA_calculate_bioavailability — absolute F from auc_po, dose_po, auc_iv, dose_iv (see Step 4).

Step 3 — Interpret the parameters

Parameter	Meaning	Notes / sanity
Cmax / Tmax	Peak concentration & time to peak — absorption rate/extent.	For IV bolus Cmax is at t=0; a later Tmax means absorption (oral) or distribution.
AUC0-t / AUC0-∞	Total exposure (area under the curve). The key exposure metric.	AUC0-∞ extrapolates the tail using Clast/lambda_z.
AUC_extrapolation_pct	% of AUC0-∞ that was extrapolated beyond the last point.	>20% → AUC0-∞ (and anything derived from it) is unreliable; report AUC0-last instead and note insufficient sampling.
lambda_z / t_half	Terminal elimination rate constant and half-life.	Trust only if r_squared_terminal_fit ≥ ~0.95 and ≥3 terminal points were used.
CL (clearance)	Volume cleared per time = Dose/AUC0-∞ (IV).	From oral data this is CL/F (apparent).
Vd	Volume of distribution = CL/lambda_z (IV).	From oral data this is Vd/F (apparent).
MRT	Mean residence time.	Longer MRT = slower overall elimination.

Step 4 — Absolute bioavailability (F)

F needs the same drug given both IV and orally (ideally same subjects, dose-normalized):

tu run NCA_calculate_bioavailability '{"auc_po":35.0,"dose_po":200,"auc_iv":43.4,"dose_iv":100}'

F = (AUC_po / Dose_po) / (AUC_iv / Dose_iv). Report as a fraction or %. F near 1 = well absorbed; low F = poor absorption or high first-pass metabolism. F > 1 signals a data/dosing error (recheck units and doses).

Step 5 — Quality gotchas (state these)

• Extrapolation >20% → don't report AUC0-∞/CL/Vd as reliable; the profile wasn't followed long enough.
• Bad terminal fit (r_squared_terminal_fit < 0.9, or <3 tail points) → half-life is unreliable.
• CL/Vd from oral data are apparent (CL/F, Vd/F) — never present them as true clearance/volume without IV data.
• Units drive CL/Vd — a wrong conc unit silently scales them. Always check the returned units block.
• Flip-flop kinetics (absorption slower than elimination) makes the "terminal" slope reflect absorption, not elimination — suspect it when oral t½ ≫ IV t½.

Honest limitations

• NCA is model-independent and robust but gives no mechanistic structure (no separate absorption/distribution rate constants) — use NCA_fit_one_compartment or population PK for that.
• AUC accuracy depends entirely on sampling density around Cmax and in the terminal phase.
• Single-dose assumptions; for steady state analyze one interval (AUC0-τ) and accumulation separately.

Related skills

• tooluniverse-admet-prediction — predict ADME properties from structure (no measured data).
• tooluniverse-dose-response — IC50/EC50 potency from concentration-response (not time-course).
• tooluniverse-statistical-modeling — compare PK parameters across groups.