Pharmacokinetic Modeling

Undersampling Bias on Cmax and Tmax Estimation

In Pharmacokinetic studies, researchers use a controlled research environment to determine the biological fate of a pharmaceutical after administration. In practice, this means determining the typical plasma concentration of the drug from the moment of administration until effective elimination of the drug from the body. From this typical profile, researchers can predict useful clinical metrics like the predicted maximum concentration (Cmax) of the pharmaceutical and the time it takes for the drug to reach peak plasma concentration (Tmax ) after administration.


The plasma concentration curve of orally, subcutaneously, topically, and intramuscularly administered pharmaceuticals generally follow three distinct phases. The first phase is the absorption phase or the period in which the pharmaceutical is still actively being absorbed by the patient. The second phase is the distribution phase or the period in which the pharmaceutical is no longer being actively absorbed and the drug reaches peak plasma concentration. In the distribution phase the pharmaceutical also begins to saturate peripheral compartments to the plasma volume. Following the distribution phase, the pharmaceutical concentration follows an exponential decay as the drug is eliminated from the body through either metabolic processes or excretion through organs such as the liver or kidneys.


Undersampling in either the absorption or distribution phase produces predictable biases in Cmax and Tmax estimation. When the plasma concentration is undersampled in the absorption phase, Tmax is mispredicted. When the plasma concentration is undersampled in the distribution phase, Cmax is mispredicted. To demonstrate that visually, we’ve prepared a convenient, simple web app that allows the user to add and remove the absorption and distribution phase from the sampling schedule of a simulated experiment. One can observe the way in which the undersampling bias the predictions of the calculation of Cmax and Tmax. Population predictions are dynamically generated using non-linear mixed-effects modeling on the simulated samples.