## Fantastic PK parameters and where to find them [NCA / SHAM]

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.

order momentum (why to limit ourselves by first order? There could be second or third order as well...).

The concentration at the end of the intended dosing interval (

The

Note that currently in Phoenix there are no direct possibility to calculate T

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

3). The calculation of MDT could be as follows: t

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?

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**is referred sometimes to be more appropriate in BE studies than C_{max}/AUC_{max}cause it has much lower variability (here we discuss C_{max}/AUC_{last}but not C_{max}/AUC_{inf}which is worse^{1}). 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*). The question is what time should be the end time of the calculation? It could be a fixed value (like 72 h), T_{max}'^{2}_{max}or common^{3}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-thorder 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 approaches^{4}to use MRT instead of T_{1/2}in order to choose the appropriate washout period.**C**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 1988_{apical}^{5}and was defined as the arithmetic mean of the concentrations within a 95% confidence interval of C_{max}(i.e.,*'not distinguishable from C*). The appropriate time t_{max}at the 5% level of statistical probability by the assay used'_{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**) should serve as an analogue of C_{τ}_{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 ways^{7}to define it.**T**- parameters named as "Therapeutic response" (_{50%lower}, T_{50%upper}, T_{50%between}(half-value duration) or T_{75%lower}, T_{75%upper}*'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 article^{9}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?

- [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

—

"Being in minority, even a minority of one, did not make you mad"

"Being in minority, even a minority of one, did not make you mad"

### Complete thread:

- Fantastic PK parameters and where to find themAstea 2020-06-12 14:22 [NCA / SHAM]
- Fantastic post 👍🏽 Helmut 2020-06-12 16:23
- Rattleback Astea 2020-06-13 10:17
- Chatter Helmut 2020-06-13 12:28
- Reinventing the Hula-Hoop Astea 2020-06-16 01:33
- Hula-Hoop references Helmut 2020-06-16 13:07
- Prof. Keller vs. Yamaoka mittyri 2020-06-17 14:28
- SHAM(e) math Astea 2020-06-23 14:41
- SHAM(e) math Helmut 2020-06-23 15:55
- OT: Möbius strip Astea 2020-06-23 21:41
- OT: Möbius strip Helmut 2020-06-24 11:29

- OT: Möbius strip Astea 2020-06-23 21:41

- SHAM(e) math Helmut 2020-06-23 15:55

- SHAM(e) math Astea 2020-06-23 14:41

- Prof. Keller vs. Yamaoka mittyri 2020-06-17 14:28

- Hula-Hoop references Helmut 2020-06-16 13:07

- Reinventing the Hula-Hoop Astea 2020-06-16 01:33

- Chatter Helmut 2020-06-13 12:28

- Rattleback Astea 2020-06-13 10:17
- More stuff Helmut 2020-06-13 15:28
- MRT and Gravity duration mittyri 2020-06-14 22:24
- Fantastic PK parameters and where to find them ElMaestro 2020-06-16 09:46
- Cauchy distribution mittyri 2020-06-16 10:54
- Cauchy distribution Helmut 2020-06-16 13:14
- Cauchy distribution ElMaestro 2020-06-20 10:33
- noncentral normal ratio mittyri 2020-06-20 23:04

- Cauchy distribution mittyri 2020-06-16 10:54

- Fantastic post 👍🏽 Helmut 2020-06-12 16:23