Estimate One Compartment Parameters
IV Bolus  Linear One Compartment
A dose of 100 mg was administered to a healthy volunteer. Seven blood samples were collected at 1, 2, 3, 4, 6, 10, and 12 hours. Plasma was separated from each blood sample and analyzed for drug concentration. The collected data are shown in the table below.
Time (hr)

Cp (mg/L)

1 
1.66 
2 
1.31 
3 
1.01 
4 
0.82 
6 
0.48 
10 
0.16 
12 
0.1 
The table above provides a set of data for you to analyze. Using these data you should be able to estimate the apparent volume of distribution for the drug and the elimination rate constant. First graph the data on semilog graph paper. Put a straight line thorugh the data. 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. Estimate the intercept on the left and right extremes of the line. The intercept on the left on the yaxis is Cp(0) with units of mg/L.
Your objective is to estimate kel, V, t_{1/2} and Clearance.
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Some Equations:
Rearranging this equation gives an equation for V. The apparent volume of distribution can be estimated from the equation:
Next we can calculate the kel (the elimination rate constant) from the slope (using the natural log, ln, version) as:
And t_{1/2} and total body clearance (CL)
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