Pharmacokinetics: Elimination Half-Life

One-compartment IV bolus. Assay plasma C at several times, fit ln C versus t, and recover t₁/₂ = ln 2 / k_el. Clearance is k_el V_c once V_c is known.

University / research· 24 min·Related simulator: Biophysics, Fluids & GeosciencePharmacokinetics: 1-/2-Compartment

Goal

Determine the terminal half-life from C = C₀ e^(−k_el t). The slope of ln C versus t is −k_el, so t₁/₂ = ln 2 / (−slope).

Equipment

IV bolus (known dose)
Known V_c
Plasma assay
Clock

Experiment

One-compartment IV bolus. No live plasma C on the bench.

Known dose D = 500 mg and central volume V_c = 42 L. One-compartment IV bolus. Plasma C appears on the assay only after you record.

Assay time tt = 4.0 h

Assay: no reading

Record at least 6 times t across 0.5–18 h, then fit ln C versus t.

Measurements

№	t h	C mg/L	ln C
No measurements yet — take your first reading.

Data processing

Add at least 2 measurements to compute the fit.

Uncertainty

Lab report

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Pharmacokinetics: Elimination Half-Life

Generated: 24 Aug 2026, 22:30

Goal

Determine the terminal half-life from C = C₀ e^(−k_el t). The slope of ln C versus t is −k_el, so t₁/₂ = ln 2 / (−slope).

Measurement table

#	t (h)	C (mg/L)	ln C
No measurements yet — take your first reading.

Fit and derived value

Add at least 2 measurements to compute the fit.

Conclusion

The fitted half-life agrees with ln 2 · V_c / CL. Main uncertainties: assay noise and the one-compartment bolus assumption.

PhysSandbox virtual lab — values come from your session; add your own discussion of error sources.

Theory

After a bolus, one-compartment kinetics is a single exponential. Dose and V_c are known; CL and t₁/₂ are hidden. The bench never prints terminal t₁/₂, AUC or a loading dose.

Procedure

Dose and V_c are fixed and known. You only change the assay time t after the bolus.
Record the plasma concentration C. Small assay noise is added. There is no live t₁/₂ or AUC.
The notebook computes ln C. Repeat for at least 6 times from about 0.5 h to 18 h.
Fit ln C versus t; t₁/₂ = ln 2 / (−slope). Compare with the reference.

Conclusion

The fitted half-life agrees with ln 2 · V_c / CL. Main uncertainties: assay noise and the one-compartment bolus assumption.