# Determine A, B, α, β from IV Data using the Method of Residuals

## IV Bolus Data - Linear Two Compartment Model

An IV Bolus dose of 250 mg was administered to a healthy volunteer. Blood samples were collected and 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) 0.25 3.32 0.5 2.69 0.75 2.38 1 2.21 1.25 2.1 1.5 2.02 2 1.89 4 1.5 6 1.19 9 0.84 12 0.59

The first step is to graph the data on semi-log graph paper and draw the Cplate line through the later data points and calculate the slope and intercept and thus β and B. The data above were calculated using the equations:

Equation 30.31 Drug Concentration, Cp, after IV bolus dose - Two compartment

The table above provides a set of data for you to analyze. Using these data you should be able to estimate the slow rate constant, the β rate constant. You can then calculate the residual as the difference between early observed drug concentration values and the extrapolated Cplate values. The plot of this residual on semi-log graph paper then provides an estimate of the faster rate constant, the α rate constant.

Estimate A, B, α and β. Does the ratio of α to β satisfy the requirement of the method of residuals?

If you want to see how the program graphs the data and performs the first step click the button below. The program will calculate the kel and intercept.

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