# AUC Calculation using Trapezoidal Rule

## IV Bolus - Linear One Compartment

A dose of 500 mg was administered to healthy volunteer. Seven blood samples were collected at 0.5, 1, 2, 4, 6, 8, 10 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) Δ (AUC mg.hr/L) AUC (mg.hr/L) 0 0.5 7.69 1 8.03 2 5.99 4 3.53 6 2.29 8 1.56 10 0.86 ∞

The table above provides a set of data for you to analyze. Use these data with the trapezoidal rule shown in the equations below to calculate each AUC segment including the last segment. The first segment is calculated using the concentration at time zero calculated by (back) extrapolation from the data provided. The data should be plotted on semi-log graph paper and a best-fit line drawn through the data. The point where this line crosses the y-axis is the y intercept or your estimate of Cp(0). Use a point on the other end of the line and calculate kel with the equation below. Estimate the area from zero to the last data point using the trapezoidal rule. Add the area for the last segment to get the total area under the curve.

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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 Useful Equations

Don't forget the first and last segments. You will need to extrapolate the concentration back to the intercept for the first segment. You will also need kel to calculate the last segment:

Calculate kel from points on the best-fit line.

Last update: Tue 7 Apr 2020 06:09:59 pm
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