How are MRT and Vss calculated after IV dosing at steady-state by PKNCA?

[JoannaPeng]

A question using IV infusion steady-state data. Doses are 2 weeks (336 hrs) apart, and after the 5th dose (DOSE.NUM=5), steady state is reached.

my.conc <- PKNCAconc(conc, DV~Time|DOSE.NUM+SUBJID)

my.dose <- PKNCAdose(dose, DOSE~Time|DOSE.NUM+SUBJID, route="intravascular", duration="EXDUR")

my.intervals <-
data.frame(
DOSE.NUM=c(1, 5),
start=0,
end=c(Inf, 336),
half.life=TRUE,
auclast=TRUE,
aucinf.obs=c(TRUE, FALSE),
cl.obs=c(TRUE, FALSE),
cl.last=c(FALSE, TRUE),
vss.iv.obs=c(TRUE, FALSE),
vss.iv.last=c(FALSE, TRUE),
mrt.iv.obs=c(TRUE, FALSE),
mrt.iv.last=c(FALSE, TRUE)
)

How are vss.iv.last and mrt.iv.last after the 5th dose (at steady state) calculated using PK.NCA? Is mrt.iv.last calculated as AUMClast/AUClast? vss.iv.last should be calculated as MRTINFCL where CL is cl.last. Is MRTINF calculated by default and used to derive vss.iv.last, even though only mrt.iv.last is specified in the code above? For MRTINF, is the following equation used: MRTINF = (AUMCtau +tau[AUCinf - AUCtau])/AUCtau, where AUCinf is for the profile at steady-state and extrapolated to infinity? And what happens when a subject only had partial sample collection and the last sample is 168 hrs post the 5th dose, not 336 hrs? In this case, AUClast and AUMClast are different from AUCtau and AUMCtau, respectively. Then all the calculations based on AUCtau and AUMCtau (e.g., for CL and Vss) are not valid any more. I think PKNCA still reports CL and Vss values in this case, but maybe shouldn't? Do you happen to know how Phoenix WNL handles this case?

[billdenney]

1. How are vss.iv.last and mrt.iv.last after the 5th dose (at steady state) calculated using PK.NCA?
   1. The parameters are calculated the same way regardless of the number of doses. (More of the answer in the next quesstion since that is more specific to the way that the parameters are calculated.
2. Is mrt.iv.last calculated as AUMClast/AUClast? vss.iv.last should be calculated as MRTINFCL where CL is cl.last. Is MRTINF calculated by default and used to derive vss.iv.last, even though only mrt.iv.last is specified in the code above?
   1. mrt.iv.last (and all the .last parameters) are calculated through tlast, regardless of the number of doses. PKNCA assumes that the requested parameter is the one that you want, so it does not make inference about the parameter you are asking for; it generates the parameter requested. mrt.iv.last is calculated as aumc.last/auc.last - dose.duration/2. The .inf versions of the parameters are provided through the parameters whose names end in .obs or .pred because they correspond to AUCinf,obs and AUCinf,pred. The parameters are documented at http://billdenney.github.io/pknca/articles/Selection-of-Calculation-Intervals.html#parameters-available-for-calculation-in-an-interval-1 (and any suggestions to improve documentation are helpful!).
3. For MRTINF, is the following equation used: MRTINF = (AUMCtau +tau[AUCinf - AUCtau])/AUCtau, where AUCinf is for the profile at steady-state and extrapolated to infinity?
   1. That is the equation for MRT at steady-state when you have a single-dose AUC to infinity as well. It accounts for nonlinearity in dosing, but it is not required when PK are linear. It is also a secondary PK parameter (it requires information from both a single dose profile to infinity and a multi-dose profile; secondary because it requires information other than just concentration or amount and time for a single interval). Unfortunately, secondary parameters are not yet supported (related to #76).
4. And what happens when a subject only had partial sample collection and the last sample is 168 hrs post the 5th dose, not 336 hrs? In this case, AUClast and AUMClast are different from AUCtau and AUMCtau, respectively. Then all the calculations based on AUCtau and AUMCtau (e.g., for CL and Vss) are not valid any more. I think PKNCA still reports CL and Vss values in this case, but maybe shouldn't?
   1. As mentioned in question 2, PKNCA assumes that the requested parameter is the one that you want. This looks like you're looking for a vss.int parameter. The .int parameters are intended to be used at steady-state to extrapolate or interpolate to the end of the dosing interval. It looks like the vss.int family of functions is missing. I'll open a separate issue to create those.
5. Do you happen to know how Phoenix WNL handles this case?
   1. I don't have access to WNL, so I don't know. I do recall that in general, WNL takes the parameters for calculation from the model selected, but I don't know specifics for this case.

Please let me know if I missed one of your questions.

[JoannaPeng]

For bullet point number 3, AUCinf is actually from the multiple dosing starting from the start of that dosing interval and extrapolated to infinity, not from a single dose, which is a little unusual for this parameter. I was confused about this myself before, but Eq. (11) from the attachment makes it clear (where Ntau is Eq. 11 is the end of the last [Nth] dosing interval). first-page-pdf (MRT equation_William Jusko).pdf ,

[billdenney]

The second paragraph of the paper indicates that it does not require anything beyond the end of the last dose and specifically indicates that the calculation does not require concentrations after tau in a steady-state dosing interval: "In this report a simplified method which extends the above principles is proposed for calculating MRT and Vd,, during multiple dosing. This approach may shorten the time required for measuring MRT and Vdss, since it involves measuring plasma concentrations only up to the time when steady state is reached."

Equation 12 removes the requirement of concentrations after the end of the last steady-state dosing interval.

I will need to look into this more to confirm what should happen.

[JoannaPeng]

It may be useful to simulate the concentration vs time after multiple dosing to steady state and calculate MRT and Vss for the 1st dose and at s.s, and see whether you will get the same Vss value.

On Tue, Jul 6, 2021 at 6:32 AM Bill Denney @.***> wrote:

The second paragraph of the paper indicates that it does not require anything beyond the end of the last dose and specifically indicates that the calculation does not require concentrations after tau in a steady-state dosing interval: "In this report a simplified method which extends the above principles is proposed for calculating MRT and Vd,, during multiple dosing. This approach may shorten the time required for measuring MRT and Vdss, since it involves measuring plasma concentrations only up to the time when steady state is reached."

Equation 12 removes the requirement of concentrations after the end of the last steady-state dosing interval.

I will need to look into this more to confirm what should happen.

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