Bioequivalence and Bioavailability Forum

Dear all!
While reading the forum I sometimes face to the statements that other PK parameters should be used in future researches for SD studies. Below is my collection of stange or rare parameters. I would be grateful if you'll comment on their properties, details of calculation and the perspectives of its using.

C_max/AUC is referred sometimes to be more appropriate in BE studies than C_max cause it has much lower variability (here we discuss C_max/AUC_last but not C_max/AUC_inf which is worse¹). For decades it was used to be the third primary PK parameter in russian studies but several years ago it became unfashionable. In the absolute majority of studies it had no impact on the results until C_max and AUC rules the decision. Even when bioequivalence was not proven for C_max and AUC C_max/AUC could be within the BE limits. The distribution type of the function is also questionable (ratio of log-normal - paranormal ?).

pAUC (partial AUC, truncated AUC), index of early exposure, as was discussed in the parallel thread could be more sensitive than AUC_last ('pAUC was always more sensitive than C_max'²). The question is what time should be the end time of the calculation? It could be a fixed value (like 72 h), T_max or common³ T_last, T_low (AUC_low, AUC_between)... The time should be related to clinically relevant pharmacodynamic measure. What are their advantages?

AUMC (first order momentum, the area under the curve 'Concentration*time-time'). If we'll look at the physics analogy - the first-order momentum for the plain figure is the static momentum which defines the center of mass coordinates, while the second-order momentum is moment of inertia. The definition could be generalised to the n-th
order momentum (why to limit ourselves by first order? There could be second or third order as well...).

MRT is a most common PK parameters that compels to look at the AUMC. There existed approaches⁴ to use MRT instead of T_1/2 in order to choose the appropriate washout period.

C_apical was invented in order to explore the shape of the peak more precisely. As far as I understood it was first mentioned in an article in 1988⁵ and was defined as the arithmetic mean of the concentrations within a 95% confidence interval of C_max (i.e., 'not distinguishable from C_max at the 5% level of statistical probability by the assay used'). The appropriate time t_{ap lower} and t_{ap high}, as well as apical duration were also discussed. The mean 20% apical time (arithmetic mean of the times associated with the concentrations within 20% of C_max) and the appropriate time parameters were also mentioned in the article. In the later publications C_apical was defined as the arithmetic mean of concentrations at some level (e.g.25% or 50% but not 95% CI!) below C_max. I've heard that this parameter was figured out as one of the perspective PK parameters from SD studies while discussing the necessity of multiple dose studies in BE testing, but I could find only few articles that deal with it. If C_apical is so promising parameter, why can't I find any trials with it in results (excepting [6] and a paper on controlled release gastroretentive dosage forms tested on dogs). Or my search methods are too poor? I would be grateful if anyone will give an example of it's calculation.

The concentration at the end of the intended dosing interval (C_τ) should serve as an analogue of C_min with lack of multiple dose studies.

The lag time matters when we deal with delayed-release formulations. Note that Phoenix defines it as time of observation prior to the first observation with a measurable (non-zero) concentration but not the time to the first observation with a measurable concentration. There could also be other ways⁷ to define it.

T_50%lower, T_50%upper, T_50%between (half-value duration) or T_75%lower, T_75%upper - parameters named as "Therapeutic response" ('Where it exists, consideration must be given to the "therapeutic window."')⁸. But aren't there limitations that could not afford to make a statement of any correlation between plasma concentrations and effect? The listed parameters can also be seen in the biosimilar studies.
Note that currently in Phoenix there are no direct possibility to calculate T_50%late or T_50%early as inter­sections.

MDT - midpoint duration time (midpoint of half-value duration). In the original article⁹ of Laszlo Endrenyi and Laszlo Tothfalusi the picture is listed in order to help to understand the meaning of the calculattion. The graph on the picture is pretty simple.
But may I have a question - do your really ever deal with such 'handsome curves'? Me - not.. My personal experience gives me an idea that the majority of individual curves look like "uncombed hedgehogs". How to define MDT for such a
curve for example (modified release or/and endogenous drug)?

I guess there may be no less than three opinions:
1). The calculation of MDT and it's interpretation for the following case is impossible
2). The calculation of MDT could be as the follows: t_50%lower+1/2*t_50%between, where t
_50%between - time between the first and the last point where C=50% C_max
3). The calculation of MDT could be as follows: t_50%lower+1/2*t'_50%between, where t'_50%between - overall time below C=50% C_max.


Usually listed strange PK objects pop up when we deal with modified release products. But what do you think about 'nice to knowing' them for IR products?

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[1] Tothfalusi L, Endrenyi L. Without extrapolation, Cmax/AUC is an effective metric in investigations of bioequivalence. Pharm Res. 1995;12(6):937-42. doi:10.1023/A:1016237826520
[2] Vincze I, Endrenyi L, Tothfalusi L. Bioequivalence metrics for absorption rates: linearity, specificity, sensitivity. Acta Pharm Hung. 2019;89(1):17–21. doi:10.33892/aph.2019.89.17-21
[3] Fisher D, Kramer W, Burmeister Getz E. Evaluation of a Scenario in Which Estimates of Bioequivalence Are Biased and a Proposed Solution: tlast (Common). J Clin Pharm. 2016; 56(7): 794–800. doi:10.1002/jcph.663
[4] Grabowski T, Gad SC, Jaroszewski JJ, Guelen P, Deterministic chaos and wash-out determination in crossover trials, Int J of Pharmacokinetics, V. 1, N. 1, doi:10.4155/ipk.16.1
[5] Pollack PT, Freeman DJ, Carruthers SG. Mean apical concentration and duration in the comparative bioavailability of slowly absorbed and eliminated drug preparations. J Pharm Sci. 1988;77:477–80.
[6] Bialer M, Arcavi L, Susann S, Volosov A, Yacobi A, Moros D, et al. Existing and new criteria for bioequivalence evaluation of new controlled release (CR) products of carbamazepine. Epilepsy Res. 1998;32:371–8.
[7] Czismadia F, L Endrényi. Model-independent estimation of lag-times with first-order absorption and disposition. J Pharm Sci 87, 608–12 (1998)
[8] Skelly JP, Barr WH. Biopharmaceutic considerations in designing and evaluating novel drug delivery systems. Clin Res Pract Drug Reg Aff. 1985;3(4):501–39.doi:10.3109/10601338509051086
[9] Endrenyi L, Tothfalusi L, Metrics for the Evaluation of Bioequivalence of Modified-Release Formulations, The AAPS Journal, Vol. 14, No. 4, December 2012, doi:10.1208/s12248-012-9396-8