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Equation 19.3.1 Concentration versus time after an IV Bolus Dose, Two Compartment Model
By definition α is greater than β then as t approaches ∞, e-α • t approaches 0 faster than e-β • t. Therefore if the ratio α/β is large enough (greater than 5) the terminal data points will fall on the line
Equation 19.3.2 Equation for Cplate versus time
This equation is similar to the equation for the late plasma concentration values after oral administration with a one compartment model. This will be a straight line if plotted on semi-log graph paper.
Figure 19.3.1 Semi-Log Plot of Cp Versus Time Showing Cplate Extrapolated Back to B
From the slope of this line a value of β can be determined.
Equation 19.3.3 Determining β from the Cplate Line
The units for β and α, below, are reciprocal time, for example min-1, hr-1, etc.
The difference between the Cplate values (red line) at early times and the actual data at early times is again termed the 'residual'
Equation 19.3.4 Equation for Residual versus time
Figure 19.3.2 Semi-Log Plot of Cp Versus Time Showing Residual Line and Cplate Line
Click on the figure to view as an interactive graph
The slope of the residual line (green line) will provide the value of α and A can be estimated as the intercept of the concentration axis (y-axis). A more accurate value for the α value can be determined by expanding the scale on the time axis (Figure 19.3.3). Don't forget to use the new time values when calculating α from the equation
Equation 19.3.5 Determining α from the Residual Line
Figure 19.3.3 Semi-Log Plot of Cp Versus Time Showing Residual Line and Cp Data - NOTE the expansion of the time axis (x axis)
Equation 19.3.6 Converting from A, B, α & β to kel, k12 & k21