Extravascular administration: monitoring drug in urine

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

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:

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

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

Sigma-Minus Method: Example Time interval (hr) Volume (ml) Concentration (mg/ml)

Sigma-Minus Method: 1- Calculate cumulative amount of drug eliminated Time interval (hr) Volume (ml) Concentration (mg/ml) Amount (mg) Cumulative Amount (mg)

Sigma-Minus Method: 2- Calculate amount remaining to be excreted (ARE) Time interval (hr) Amount (mg) Cumulative Amount (mg) ARE (mg)

Sigma-Minus Method: 3- Plot time (end of interval) vs. log(ARE) Time (hr) ARE (mg) Terminal phase (straight line)

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

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

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:

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:

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

The rate of excretion method: Example Time interval (hr) Volume (ml) Concentration (mg/ml)

The rate method: 1- Calculate amount of drug eliminated Time interval (hr) Volume (ml) Concentration (mg/ml) Amount (mg)

The rate method: 2- Calculate the change in time Time interval (hr) Volume (ml) Concentration (mg/ml) Amount (mg) Δt (hr)

The rate method: 3- Calculate the rate of urinary excretion Time interval (hr) Volume (ml) Concentration (mg/ml) Amount (mg) Δt (hr) mg/hr

The rate method: 4- Plot time (mid of interval) vs. log(dXu/dt) Time (h) mg/hr Terminal phase (straight line)

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

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