Rate of Excretion versus Midpoint Time Plot

Equation 12.4.1 Rate of Change of U versus Time

Taking the logarithms of both sides gives:-

Equation 12.4.2 ln (dU/dt) versus Time

Thus by plotting ln (dU/dt) versus time you should get a straight line with a slope of - kel.

It may look like a strange way of plotting the data, but actually it's quite convenient to use because urine data results are collected as an amount of drug excreted during a time interval. The amount excreted is the product of the volume of urine voided and the concentration of drug in the sample. Again, this is a rate measurement. Since we estimate dU/dt as ΔU/Δt, an average rate of excretion over the collection interval, the t value used with this plot is the time at the midpoint of the collection interval.

The working equations then become:

Equation 12.4.3 Rate of Excretion versus Midpoint Time

Analysis of 'real' data may show considerable scatter in the rate of excretion plot. Thus positioning the straight line on a semi-log plot may be difficult. In practical terms it is difficult to get a lot of early times points unless the subjects are catheterized and even then early times may be difficult to interpret. A significant advantage of the rate of excretion plot is that each data point is essentially independent. A missed sample or data points is not critical to the analysis.

Figure 12.4.1 Semi-log Plot of Rate of Excretion versus Time

Click on the figure to view the Java Applet window
Java Applet as a Linear Plot

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Copyright 2001-3 David W. A. Bourne (david@boomer.org)