Background: Theophylline
Theophylline is a methylxanthine bronchodilator used in the treatment of asthma and COPD. It has a narrow therapeutic index (10–20 μg/mL), making precise PK characterization essential. The Theophylline Subject 1 dataset from Gabrielsson & Weiner's textbook is one of the most widely used validation datasets in pharmacokinetic software.
Drug: Theophylline · Dose: 319.992 mg (oral) · Route: Extravascular
Subject: Subject 1 · Matrix: Plasma · Time Points: 11 samples (0–24.37 h)
1 The Raw Data
Here are the 11 concentration-time data points for Theophylline Subject 1:
| Point | Time (h) | Concentration (ng/mL) | Phase |
|---|---|---|---|
| 1 | 0.00 | 0.74 | Baseline |
| 2 | 0.25 | 2.84 | ↑ Absorption |
| 3 | 0.57 | 6.57 | ↑ Absorption |
| 4 | 1.12 | 10.50 | ★ Cmax |
| 5 | 2.02 | 9.66 | ↓ Distribution |
| 6 | 3.82 | 8.58 | ↓ Distribution |
| 7 | 5.10 | 8.36 | ↓ Elimination |
| 8 | 7.03 | 7.47 | ↓ Elimination |
| 9 | 9.05 | 6.89 | ↓ Elimination |
| 10 | 12.12 | 5.94 | ↓ Terminal |
| 11 | 24.37 | 3.28 | ↓ Terminal |
2 Observed Parameters
Some parameters can be read directly from the data without any computation:
Directly Observed
3 AUC Calculation
Using the Linear-up Log-down trapezoidal method:
- Points 1→4 (ascending): Linear trapezoidal
- Points 4→11 (descending): Log-linear trapezoidal
Computing each interval and summing gives us the total AUC from time 0 to the last measured time point (24.37 h):
AUC Parameters
The extrapolated fraction exceeds the typical 20% threshold. This indicates that the sampling window may not have been long enough to fully characterize the terminal phase. In practice, you would extend sampling or note this caveat when reporting AUC₀₋∞. This is a known characteristic of this particular dataset.
4 Terminal Phase Analysis
PK-Swift's Best Fit algorithm selects the optimal terminal points by evaluating all subsets of ≥ 3 consecutive points after Tmax and choosing the one with the highest adjusted R².
Terminal Phase Regression
5 Derived PK Parameters
Using dose (319.992 mg), AUC₀₋∞, and λz, we derive:
Derived Parameters
6 Clinical Interpretation
Cmax (10.50 ng/mL) — Within the therapeutic range (10–20 μg/mL for theophylline), indicating adequate drug levels for bronchodilation.
Half-life (14.3 h) — Typical for theophylline in adult non-smokers. Smokers typically have shorter half-lives (4–5 h) due to CYP1A2 induction. This long half-life supports once- or twice-daily dosing regimens.
CL/F (1.49 L/h) — Consistent with published values for oral theophylline clearance. Note: this is apparent clearance (CL/F) which includes the effect of bioavailability.
Vz/F (30.7 L) — Theophylline distributes into approximately 0.5 L/kg of body weight, suggesting moderate tissue distribution.
7 Validation Summary
All computed parameters agree with published textbook reference values within expected tolerances. PK-Swift's automated Validation Benchmark runs 18 tests on this exact dataset and achieves >99% geometric mean accuracy.
| Parameter | Computed | Reference | Status |
|---|---|---|---|
| Cmax | 10.50 | 10.50 | ✓ PASS |
| Tmax | 1.12 | 1.12 | ✓ PASS |
| AUClast | 147.24 | 147.24 | ✓ PASS |
| AUCinf | 214.92 | 214.92 | ✓ PASS |
| t½ | 14.30 | 14.30 | ✓ PASS |
| CL/F | 1.489 | 1.489 | ✓ PASS |
| Vz/F | 30.72 | 30.72 | ✓ PASS |
References
- Gabrielsson J, Weiner D. Pharmacokinetic & Pharmacodynamic Data Analysis: Concepts and Applications. 5th ed. Stockholm: Swedish Pharmaceutical Press; 2016.
- Rowland M, Tozer TN. Clinical Pharmacokinetics and Pharmacodynamics: Concepts and Applications. 4th ed. Philadelphia: Lippincott Williams & Wilkins; 2011.
- Gibaldi M, Perrier D. Pharmacokinetics. 2nd ed. New York: Marcel Dekker; 1982.
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