- On 7 Apr 1997 at 22:04:00, Bill McNaughton (hossack.at.nbnet.nb.ca) sent the message

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A QUESTION FOR ANYONE WITH THE PATIENCE FOR A NEWCOMER TO PK/PD. IN A

STANDARD STUDY COMPARING BLOOD LEVELS OF A BRAND NAME AND GENERIC DRUG,

IS A POSSIBLE TO GET VALUES FOR AUC infinity THAT ARE LESS THAN THE

VALUES OBTAINED FOR AUCt? - On 9 Apr 1997 at 12:47:11, "David Nix" (nix.-at-.Pharmacy.Arizona.EDU) sent the message

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No, it is not possible to have values of AUC(0-inf) < AUC(0-t).

AUC(0-inf) = AUC(0-t*) + C*/ke where C* is the last measured

concentration at time (t*) and ke is the terminal elimination rate

constant. My guess is that ke was entered as a negative value. ke

is determined from the slope of the terminal linear portion of the

LN (Conc) vs time curve. The slope will always be negative since

concentrations are declining. It is sometimes an art in determining

which points to use in determining the terminal slope. The terminal

elimination rate constant term implies decreasing concentrations and

therefore the negative is not required (ke is always positve,

-(slope))

David - On 9 Apr 1997 at 12:47:30, Bob Phair (rphair.aaa.ix.netcom.com) sent the message

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The partial area under the curve (AUCt) is the area from t=0 to t=t.

AUCinfinity is the area from t=0 to t=infinity. Since there can be no

negative contributions to the AUC at any time after t (or before t, for

that matter) AUCinfinity is always greater than AUCt.

Of course, one might make the mistake of plotting the data on linear,

instead of semi-log, paper, and then extrapolating a fast (apparently

terminal) exponential through the horizontal axis and thus appear to

start accumulating negative contributions to AUCinfinity. It should be

clear however that the real blood concentration can never be a negative

number, so the AUC can only increase as the integration is carried out

toward infinity.

Regards,

Bob

--

Robert D. Phair, Ph.D. rphair.aaa.ix.netcom.com

BioInformatics Services http://www.webcom.com/rphair

Partnering and Outsourcing for Computational Biology - On 9 Apr 1997 at 12:47:45, Steve Bramer (STEVEB.aaa.OTSUKA.OAPI.COM) sent the message

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It is possible and is also incorrect. Check your rules for determining half

life and extrapolation to infinity. - On 9 Apr 1997 at 12:48:37, "Aziz Karim" (AAKARI.at.msn.com) sent the message

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Dear Bill:

You have raised a very interesting point. I too have come across occasions

when AUC(inf) values were lower than AUC(t). We need to clearly define the

AUC(t) values. Is this the AUC up to the last validated measurable plasma

concentration [C(last), I call the corresponding AUC, AUC(last)] or is it the

AUC up to the last point which is below the limit of quantitation [considered

zero in AUC calculation] which I call AUC(all).

It would be highly unusual to have AUC(last) larger than AUC(inf). However, it

is possible for AUC(all) to be larger than AUC(inf). This occurs when time

span is large between the last validated plasma concentration in the

disposition phase and the next sample with concentration below quantitation.

The above is difficult to explain in words. You will get a better appreciation

if you draw a figure. I would be happy to fax you one.

As a note, I don't particularly like to use AUC(inf) for drugs with short half

lives (T1/2 = < 12 hours). The reason for this is one single concentration

[C(last)] in the beta phase has a high influence on the AUC(inf) values since

AUC(inf) = AUC(last) + [C(last)/(0.693/T1/2)]. It is simply better to

determine AUC(last) with most sensitive assay and taking blood samples for a

time period exceeding 4*T1/2.

AUC(inf) is more appropriate for drugs with long T1/2 (>24 hours) provided

that the ratio of AUC(last)/AUC(inf) exceeds) 0.80.

I hope the above will stimulate discussion on AUC determinations since this

parameter is critical in bioavailability assessment.

Regards,

Aziz Karim

aakari.-at-.msn.com - On 10 Apr 1997 at 13:31:57, Allen.E.Cato.-a-.abbott.com sent the message

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Bill,

While it is true that the actual AUC(inf) cannot be less than the actual

AUC(t), it is possible to calculate an AUC(t) value that is larger than the

calculated AUC(inf) value depending on the sampling scheme relative to the

half-life, as Dr. Karim discussed.

As a follow-up to his note on the potential inaccuracies of the calculation of

AUC(inf) for compounds with short half-lives, if variability of the low

concentrations is an issue, AUC(inf) could be extrapolated from a predicted

C(last) at the time of the last measurable concentration based on the half-life

(beta) regression. With this method, the data used to estimate half-life would

be weighted equally in the extrapolation to infinity. This method assumes that

there are adequate data to estimate the half-life relatively accurately.

Jo Cato

allen.cato.-at-.abbott.com - On 10 Apr 1997 at 13:34:03, Brinda Koneru (BRINDAK.-a-.OTSUKA.OAPI.COM) sent the message

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AUCt cannot exceed AUCinfinity since AUCinf = AUCt + C(t)/?z.

However, it is possible to get AUCinfinity < AUC(0-24) or AUC(0-48),

AUCall, etc.

If your sampling points in the terminal phase are far apart and your last

sample is BQL (and your program treats BQL samples as zero), then ?z

may be larger than the slope connecting the last 2 points which are C(t)

and 0. This will cause AUCinf to be less than AUC0-24 because in the

calculation of AUCinf, zero is not used.

Brinda K Tammara

Otsuka America Pharm. Inc.

Rockville

MD-20850 - On 10 Apr 1997 at 13:34:26, "Faruq H Noormohamed" (f.noormohamed.-at-.s1.cxwms.ac.uk) sent the message

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As indicated by several replies generated from the inquiry as to whether

one can get values of AUC(0-inf) which are less than AUC(0-t), the answer

is that in theory NO. However in practice you may come across data which

suggests that this is the case. Apart from the obvious error in

calculating AUCs. I assume you have used the correct formula for

calculating the area of trapezoids, or as David Nix pointed out you may

have used -ke rather than the absolute value of ke to calculate AUC(t-inf).

that is if you have devised you own routine for calculating the parameters.

Alternatively the problem may reside in the software package you are using

in that some software may calculate AUC(0-inf) either using the exponential

fitting parameters or alternatively use the expected concentration at time

't-last', derived from the terminal rate constant as opposed to observed

value whilst AUC(0-t) have been calculated using observed values. Bit

complicated but I hope it is clear.

Faruq H Noormohamed

Department of Therapeutics

Chelsea and Westminster Hospital

369 Fulham Road

LONDON

SW10 9NH

Tel +44 (0)181 746 8141

Fax +44 (0)181 746 8887

email f.noormohamed.at.cxwms.ac.uk

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