Fit fluctuating blood drug concentration: a beginner's first note.

In linear pharmacokinetics a blood drug concentration can be described and fitted using the equation of a sum of exponential functions, but this equation cannot exactly describe and fit a fluctuating (oscillating) blood drug concentration, which is a common phenomenon in clinical pharmacokinetic settings. Although a number of hypotheses have been provided for the phenomenon of a fluctuating blood drug concentration, a possible mathematical analysis has yet to be fully explored. In the present study we proposed several equations from other research fields to be used in pharmacokinetics. These equations contain decaying exponential sinusoidal functions and can theoretically fit a fluctuating curve. We used these equations to produce fluctuating curves. The results suggested that these equations might be suitable for use in pharmacokinetics. Furthermore, we demonstrated that the analytical solution of the differential equation system for a compartmental model can contain decaying exponential sinusoidal functions. We conclude that the analytical solution of the differential equation system for a compartmental model in pharmacokinetics is a sum of decaying exponential and sinusoidal functions rather than a sum of exponential functions, the latter one being only an approximate analytical solution of the differential equation system for a compartmental model.