Estimate Parameters from Urine versus Time Data

IV Bolus - Linear One Compartment

Using the Rate of Excretion Plot

A dose of 1000 mg was administered to a healthy volunteer. Total urine samples were collected after 2, 4, 6, 8, 10, 12, 18 and 24 hours. Samples were well mixed and analyzed for drug concentration. The volume of each sample was also recorded. The collected data are shown in the table below.

Time (hr) Urine Volume (ml) Cu (mg/ml)
2 60 3.174
4 55 2.438
6 54 1.752
8 64 1.04
10 61 0.77
12 50 0.66
18 182 0.282
24 164 0.109

The table above provides a set of data for you to analyze. Using these data you should be able to estimate the elimination rate constant for the drug and the fraction excreted as unchanged drug. First calculate the amount of unchanged drug excreted during each time interval and thus the cumulative amount excreted upto that time point, U. Calculate the rate of excretion versus the midpoint time and plot these data on semi-log graph paper. Put a straight line through the data on the semi-log plot. A best fit line. Don't try to put the line through any particular point but through all the data. The best fit line may not go through any of the points. A clear ruler helps as you can see the points above and below the line to get a good balance. Draw the line on the graph. Estimate the elimination rate constant from the slope of the line. Estimate the intercept on the left and right extreme of the line. The intercept on the y-axis (the left extreme) is ke • Dose (Units mg/hr: Rate of Excretion plot).

Your objective is to estimate kel, ke, and fe.

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Graph Paper Resources

Graph Paper in PDF Format. If you have Adobe Reader installed or Preview in Mac OS X clicking on the links below will provide the graph paper indicated.

Some Equations:

The equation for the cumulative amount excreted at time, t, after the dose is given by:
U versus time

ke is the first order excretion rate constant and kel is the 'overall' elimination rate constant.

The equation for the rate of excretion versus the midpoint time, t, is given by:

Rate of Excretion versus midpoint time

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