We used to discuss in a small group some of the ways in which pharmacokinetic parameters were determined for a given drug. In the absence of such a time slot, let me explain here the issue of determining the AUC from experimental data (plasma concentration versus time, after giving a certain single dose of drug to a patient) – this being necessary of course for determining the bioavailability of a drug.

How can we determine the AUC for a curve obtained by experimental data points, not being linear but rather representing a Bateman function (first order exponential drug absorption plus first order exponential elimination...)?

Usually you would plot the data to see whether they look reasonable and represent a curve that you expect. Then there are several options.

- Draw the curve by hand or computer, using a grid as a background and count (estimate) the grid squares “under the curve”. The number of grids is all you need usually, but knowing the area for each grid, the grid count gives you the total area in the exact dimensions (say, [mg/mL times time]).
- After drawing a curve as above, cut out the area to be measured and weigh the paper (so-called “integration paper used to be available with a rather constant weight/area. The nice thing is that this method can take care of any shape of a cirver for which you otherwise may not have a descriptive formula. Of course, the weight is just something that is proportional to the AUC, but weiging a cutout of a rectangle or square for which you can calculate the exact are in [mg/L x time] can give you an absolute value.
- I have seen engineers using some x/y tracing gadgets that run up a counter number for you as you trace around an area.
- Mathematically, use the Batement equation to fit the data points to and calculate the parameters by iterative procedures (rate constants in and out): And, after inserting the parameter estimates into the formula, integrate it between the limits of time zero to somewhere when the curve almost touches the x-axis or maybe to infinity. This would be an enormous task without computers!The plotting program called “Sigmaplot” is tremendous for such a task. The obtained integral of course is the AUC.
- Fit the data point sto a polynomial (y = a + bx + cx
^{ 2}+ dx^{3}.......) and after insertion of the parameter estimates integrate the function between the same limits as above. - Use the experimental data and generate rectangles of time intervals times PC values that approximate the AUC, and this can be easily done by using a spreadsheet calculator. That is what I would be using nowadays where I do no longer have available Sigmaplot! You can try it out, it is fun: The spreadsheet is included in your ancillary files and available on the Student Drive under my name following the Basics lectures
- After drawing a curve as above, cut out the area to be measured and weigh the paper (so-called “integration paper used to be available with a rather constant weight/area). The nice thing is that this method can take care of any shape of a curve for which you otherwise may not have a descriptive formula.
- Mathematically, use the Batement equation to fit the data points to and calculate the parameters (rate constants in and out): And, after inserting the parameter estimates into the formula, integrate it between the limits of time zero to somewhere when the curve almost touches the x-axis or maybe to infinity. This would be an enormous task without computers!The plotting program called “Sigmaplot” is tremendous for such a task. The obtained integral of course is the AUC.
- Fit the data point to a polynomial (y = a + bx + cx
^{ 2}+ dx^{3}.......) and after insertion of the parameter estimates integrate the function between the same limits. - Use the experimental data and generate rectangles of time intervals times PC values that approximate the AUC, and this can be easily done by using a spreadsheet calculator. That is what I would be using nowadays where i do no longer have available Sigmaplot! You can try it out, it is fun: The spreadsheet is included in your ancillary files and available on the Student Drive under my name following the basics lectures. File name: “CP and AUC Calculations Spreadsheet”.

One you have values for AUC, exact or proportionally, you then of course take the AUC for the i.v. administration as 100% and calculate the bioavailability for your drug in relation to that. How many times in one patient, and how many patients total? I have no idea - ask the clinical pharmacologist of a company! I know one and will let you know what he says...

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