1. Extravascular administration: monitoring drug in urine

2. Methods to compute PK parameters from urinary data 1. the ‘‘amount remaining to be excreted’’ method (ARE); also known as the sigma- minus method 2. The rate of excretion method

3. Sigma-Minus Method Amount of unchanged or excreted drug in urine (X u ) is given by: the cumulative amount of drug excreted in the urine at t = ∞ is: Substitution for and rearrangement yields:

4. Sigma-Minus Method Generally, when Ka>>K, at certain time point the absorption process ends (become negligible) as we referred earlier by the terminal phase. Previous Eqn. become: Taking the logarithm, we get: Thus the plot of vs. end of the time interval gives a line with a slope equal to –K/2.303

5. Sigma-Minus Method: Example An oral tablet with a strength of 500 mg of a drug was administered. The drug is one that is partially eliminated by urinary excretion of unchanged drug following one-compartment model distribution and first-order elimination. Using the urinary data presented in the following table, calculate elimination rate constant

6. Sigma-Minus Method: Example Time interval (hr) Volume (ml) Concentration (mg/ml) 0-2501.272 2-4252.972 4-81000.915 8-162000.280 16-241500.075 24-322000.011

7. Sigma-Minus Method: 1- Calculate cumulative amount of drug eliminated Time interval (hr) Volume (ml) Concentration (mg/ml) Amount (mg) Cumulative Amount (mg) 0-2501.272 63.6063.6 2-4252.972 74.30137.9 4-81000.915 91.50229.4 8-162000.280 56.00285.4 16-241500.075 11.25296.7 24-322000.011 2.20298.9

8. Sigma-Minus Method: 2- Calculate amount remaining to be excreted (ARE) Time interval (hr) Amount (mg) Cumulative Amount (mg) ARE (mg) 0-2 63.6063.6235.3 2-4 74.30137.9161.0 4-8 91.50229.469.5 8-16 56.00285.413.5 16-24 11.25296.72.2 24-32 2.20298.90

9. Sigma-Minus Method: 3- Plot time (end of interval) vs. log(ARE) Time (hr) ARE (mg) 2 235.3 4 161.0 8 69.5 16 13.5 24 2.2 32 0 Terminal phase (straight line)

10. Sigma-Minus Method: 4- draw the best fit line to the linear portion of the curve (terminal phase)

11. Sigma-Minus Method: Example The plot of log(ARE) vs. end of the time interval point of urine collection time gives a line with a slope equal to –K/2.303

12. The rate of excretion method substituting the value of X from previous lecture (oral equation), we get: Generally, when Ka>>K, at certain time point the absorption process ends (become negligible) as we referred earlier by the terminal phase. Previous Eqn. become:

13. The rate of excretion method Taking the logarithm, we get: Thus the plot of dXu/dt vs. mid point of urine collection time gives a line with a slope equal to –K/2.303 The total amount to be eliminated ( ) is:

14. The rate of excretion method: Example An oral tablet with a strength of 500 mg of a drug was administered. The drug is one that is partially eliminated by urinary excretion of unchanged drug following one-compartment model distribution and first-order elimination. Using the urinary data presented in the following table, calculate elimination rate constant

15. The rate of excretion method: Example Time interval (hr) Volume (ml) Concentration (mg/ml) 0-2501.272 2-4252.972 4-81000.915 8-162000.280 16-241500.075 24-322000.011

16. The rate method: 1- Calculate amount of drug eliminated Time interval (hr) Volume (ml) Concentration (mg/ml) Amount (mg) 0-2501.272 63.60 2-4252.972 74.30 4-81000.915 91.50 8-162000.280 56.00 16-241500.075 11.25 24-322000.011 2.20

17. The rate method: 2- Calculate the change in time Time interval (hr) Volume (ml) Concentration (mg/ml) Amount (mg) Δt (hr) 0-2501.272 63.602 2-4252.972 74.302 4-81000.915 91.504 8-162000.280 56.008 16-241500.075 11.258 24-322000.011 2.208

18. The rate method: 3- Calculate the rate of urinary excretion Time interval (hr) Volume (ml) Concentration (mg/ml) Amount (mg) Δt (hr) mg/hr 0-2501.27263.60231.80 2-4252.97274.30237.15 4-81000.91591.50422.88 8-162000.28056.0087.00 16-241500.07511.2581.41 24-322000.0112.2080.28

19. The rate method: 4- Plot time (mid of interval) vs. log(dXu/dt) Time (h) mg/hr 131.80 337.15 622.88 127.00 201.41 280.28 Terminal phase (straight line)

20. The rate method: 5- draw the best fit line to the linear portion of the curve (terminal phase)

21. The rate of excretion method: Example The plot of dXu/dt vs. mid point of urine collection time gives a line with a slope equal to –K/2.303