Bioequivalence and Bioavailability Forum

Dear Ohlbe & Alhas!

❝ Elimination starts at the second the drug enters the body.

Exactly. There are many processes involved, all of them are stochastic ones. In PK we retreat into the concept of ‘compartments’, because we cannot better model our body consisting of 10¹³–10¹⁴ cells. Speaking of a one-compartment model, we treat blood and all highly perfused organs (liver, brain, kidneys; partly muscles) as a (well-stired) beaker with a small hole in the bottom. We assess these processes statistically; if we talk about the half life of two hours of a drug with a molecular mass of 200 g/mol after a bolus dose of 10 mg on the average 1.506×10¹⁹ molecules will have left the systemic circulation within the first two hours. Or modifying your example (∆ input of zero duration), about 2.9×10¹⁵ molecules leave the system in the first second!¹ – or 962 ng if you prefer to weigh a bunch of molecules…
If we split the equation we can see that after an oral dose the elimination process itself is exactly the same as after a fast bolus (the concentration at t=0 is D/V_d, which I have set throughout the examples in this thread to 100/5).

An nice property of the function is the intersection of the elimination with the profile at t_max/C_max.
It’s clear why the starting point for the estimation of the half-life in the TTT-me­thod (see this post) was chosen.
Also one of Kamal Midha’s Mantras (‘Once absorption is over, formulation differences no longer apply.’)² is obviously justified (valid for ≥2×t_max).

❝ Tmax is the time when you reach a balance between absorption and elimination: before Tmax the drug enters the body faster than it is eliminated, and concentrations increase. After Tmax the drug is eliminated faster than it is absorbed, and concentrations decrease.

Almost…
In a one-compartment system both absorption and elimination are treated as constant. Therefore, there’s no faster/slower absorption/elimination throughout the profile. In the log-plot the parallel course after about 2×t_max is even more evident (in more mathematical terms after the inflection point of the first derivative; where the root of the first derivative = t_max).



@Alhas:
I strongly suggest to study one of the basic textbooks on pharmacokinetics – otherwise it will be very difficult for you to design and evaluate BA/BE-studies. I’m not always in the mood to answer “neophytes”.
If you want a quick solution I recommend David Bourne’s A First Course in Pharmacokinetics and Biopharmaceutics.

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1. Only in a Gedankenexperiment! Since the turn-around time of the circulation is about two minutes, it will take a little bit longer…
   
2. Midha KK, Hubbard JW, Rawson MJ. Retrospective evaluation of relative extent of absorption by the use of partial areas under plasma concentration versus time curves in bioequivalence studies on conventional release products. Europ J Pharm Sci 1996;4:381–4.