Problem number 1360649033
Estimate Parameters from Urine versus Time Data
IV Bolus - Linear One Compartment
A dose of 500 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)
|
|
0
|
|
|
|
2 |
73 |
1.623 |
|
4 |
74 |
1.092 |
|
6 |
71 |
0.779 |
|
8 |
86 |
0.439 |
|
10 |
65 |
0.392 |
|
12 |
69 |
0.253 |
|
18 |
238 |
0.107 |
|
24 |
213 |
0.038 |
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 ecreted during each time interval and thus the cumulative amount excreted upto that time point, U. Graph U on linear graph paper. Calculate the rate of excretion versus the midpoint time and the amount remaining to be excreted versus time and plot these data on semi-log graph paper. Put a straight line through the data on each of the semi-log plots. 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. Then you can see the points above and below the line to get a good balance. Draw the line on each graph. Estimate the elimination rate constant from the slope of each line. These may be different values. 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) or fe • Dose (Units mg; Amount remaining to be excreted).
Thus, your objective is to estimate kel, ke, and fe.
If you want the program to graph the data for you. Click this button. You should print the resulting graphs, draw a line through the data on the semi-log plots and calculate the slope and intercept and thus kel, fe and ke. Click the back arrow to get back to this page.
You can check your answer by clicking on this button (without clicking on the "Try Another Data set" button).
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To get credit for this problem print this page, work the problem and
You will have one chance to submit your answers for this problem [# 1360649033]. You can try more than once with different data to improve your grade.
Graph Paper Resources
Graph Paper in Adobe Reader (v5.0) - 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:
ke is the first order excretion rate constant and kel is 'overall' elimination rate constant.
The equation for the rate of excretion versus the midpoint time, t, is given by:
The amount remaining to be excretion (A.R.E.) versus time (at the end of the sample interval) is given by:
Last update: Wed 18 Feb 2004 03:01:18 pm
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