PHAR 7632 Homework #2 2001

Curve Fitting and Laplace Exercise

DUE 20th Feb 2001 - Not graded

Answers

The following data was collected after an I.V. bolus dose of 250 mg.

Time (hr)	Cp (mg/L)
1	7.5
2	5.2
3	2.5
5	0.85
6	0.58

Question 1. Graph the data above on semi-log graph paper. Draw a 'best-fit' line through the data point. From points at either end of this line calculate the slope and then kel, the elimination rate constant. What is the intercept (Cp(0))? What is the apparent volume of distribution? HINT Have a look at the pages 1 and 2.

Question 2. Analyse the same data using Boomer and parameter type 8.

Start Boomer. Enter 0 to enter Data from the Keyboard (Alternately you might enter 2 and then enter HW0102 as the .BAT filename). Enter 0 for normal fitting. Send output to a disk file. Enter 1 and then enter HW0102 as the .OUT filename Choose parameter type 8 for parameter 1. Enter A as the parameter name. Enter your estimate of the intercept (from Question 1 above) as the value. This is a parameter you want Boomer to adjust. Enter 1 Choose lower limit and upper limits 1/10 and 10 times the initial value. Enter 1 for the data set number, Cp for the line description and 0 for the component number. Do the same for the lamba value, i.e. the kel value from above. Enter 0 and 0 (fixed) for the lag-time. Enter -1 to exit this section. Use Damping Gauss-Newton as the fitting method (I'll explain this later). Press return twice to take the default values for DT and PC. Description: Homework #3 (and your name) Enter data from keyboard (1) Enter the 5 data pairs, x first then y. After the last data point enter -1 for x to exit this section. Enter 0 to accept data and 0 to NOT save the data. Enter 2 for the weighting function (I'll explain this later). Enter 1 and then 0 to calculate AUC Enter 2 for a graph and -1 to finish the run. Open the HW0102.OUT file and print it using a suitable font.

Question 3. Use Laplace transform method to integrate the differential equation for Component 2 in the diagram below.


[-------------]       [-------------]      [------------] 
[             ]  k1   [             ]  k2  [            ]
[ Component 1 ] ----> [ Component 2 ] ---> [ Component 3]
[             ]       [             ]      [            ]
[-------------]       [-------------]      [------------]

The dose is put into Component 1 and k1 and k2 are first order rate constants. Write the differential equations for the amount of drug (X₁ and X²) in components 1, 2 and 3. Take the Laplace of these differential equations. Solve for the Laplace of component 3. Using the table online or in the Mayersohn/Gibaldi paper back transform for X₃.