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Dear all,
I've read that MRT denotes the time it takes to eliminate the dose by 63.2%
(Biopharmaceutics and Clinical Pharmacokinetics. Milo Gibalbi. 4th edition. Lea & Febiger.
1991). However I can't find out where this percentage comes from. Does anyone know?
Kind regards,
Johan Birgersson
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The following message was posted to: PharmPK
Dear Johan,
MRT can be defined as the geometric mean of the times needed to eliminate drug molecules
(ie, residence time). At MRT, 1/e = 36.8% of molecules are still remaining and therefore
63.2% of dose is eliminated. Hope this helps.
Jack
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Johan,
This is true only for first-order elimination after IV bolus.
The ratio between AUC(0 to MRT) and AUC(MRT to inf) equals e - 1, or 1.718. =46rom here it
is easy to calculate that AUC(0 to MRT) represents 63.2% of the total AUC. To see the
detailed math you can use this reference:
Volosov A, Bialer M. Biopharm Drug Dispos. 1999 Jan; 20(1):3-9.
Hope this helps.
Andrew Volosov
Shire HGT
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Andrew,
I think you wanted to say that this percentage (63.2%) is correct only
if the PK of the drug can be best characterized by a one-compartment
model after IV bolus administration. One may add to this that it
practically never occurs as most drugs are best characterized by
multi-compartment models after IV bolus administration.
Stefan Soback
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The following message was posted to: PharmPK
Dear Johan,
1-exp(-1)=0.6312...
The statement you cite is correct for one compartment model with i.v.
administration.
It is by no means the general definition of MRT.
In general MRT is defined as expectance of time the drug molecule spend
in the body before it is eliminated:
MRT = AUMC / AUC.
If C(t)=Co*exp(-k*t), then AUC=Co/k; AUMC=Co/k^2; therefore MRT=1/k. If
you substitute t=1/k you will obtain C(MRT)=Co*exp(-1).
At t-=MRT the part of drug dose remaining in circulation is exp(-1), so
1-exp(-1) is the percentage eliminated.
Best regards,
Wojciech Jawien
Jagiellonian University
Krakow, Poland
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The following message was posted to: PharmPK
Dear Johan,
MRT can be defined as the arithmetic (not the geometric mean as
suggested by Jack Shi) of the residence times of each drug molecule in
the body, i.e. the time between administration and elimination.
For any PK model where the drug elimination is proportional to the
plasma concentration, it follows that the hazard of a molecule to be
eliminated is proportional to the plasma concentration. Therefore MRT
can be obtained by summing the product of hazard and time (AUMC), and
normalize this to the cumulative hazard (AUC). This implies that
MRT = AUMC / AUC
where AUMC is the area under the C*t versus time profile integral(0-inf) { C*t }
(C*t is the product of concentration and time)
For a one-comparment model the concentration - time profile at IV bolus
is C = C0 * exp(-k*t), so
MRT = integral(0-inf) { C*t } / integral(0-inf) { C }
= integral(0-inf) { C0 * t * exp(-k*t) } / integral(0-inf) { C0 *
exp(-k*t) }
= ( C0 / k^2 ) / (C0 / k) = 1 / k
At time t = MRT it follows: C / C0 = exp(-k*MRT) = exp(-1) = 0.367879.
Therefore a fraction 1 - 0.367879 = 0.632... = 63.2% of the dose has
been eliminated.
Jack Shi wrote:
> At MRT, 1/e = 36.8% of molecules are still remaining
OK, but where does this come from?
Andrew Volosov wrote:
> The ratio between AUC(0 to MRT) and AUC(MRT to inf) equals e - 1, or
1.718. From
> here it is easy to calculate that AUC(0 to MRT) represents 63.2% of
the total AUC.
For me this is not so easy.I understand that all this is described in
your cited paper, but I think my explanation is easier.
best regards,
Hans Proost
Johannes H. Proost
Dept. of Pharmacokinetics, Toxicology and Targeting
University Centre for Pharmacy
Antonius Deusinglaan 1
9713 AV Groningen, The Netherlands
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I think we are getting a little bit carried away in this discussion. The
63.2% is a curiosity that occurs when the (specific) drug exhibits
one-compartment model disposition after IV bolus administration. It is
not a definition of the MRT. I think the reason for this confusion
results from our general less than perfect understanding of the
differences between one-compartment and multi-compartment model PK,
which, unfortunately, has to be taken into account also in the
non-compartmental PK analysis.
One has to keep in mind that MRT = 1/K (and I suggest that we use the
capital K for clarity) only when the compound can be best characterized
by one-compartment model PK. In such case we can also utilize the
relationship t1/2 = ln2 * MRT as long as you remember the limitation. I
see a similarity here in the use of the term Vss/F. This, too, can be
determined only for compounds that exhibit one-compartment model PK
after IV bolus administration (i.e. you have to know that a priori when
dealing with non-IV administration PK). Still Vss/F is, incorrectly,
determined in quite a few papers for compounds that clearly do not meet
this criterion.
Stefan Soback
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MRT is defined as the arithmetic average (my mistake) of residence time,
and in the context of mono-exponential decline, MRT simply is the time
needed for drug concentration to decrease by 1 (natural) logarithmic
unit, whereas half-life may be thought as the median residence time.
Jack
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I certainly agree with Stefan that 63.2% has a lot to do with math, and little to do with
actual PK. Could be a good question to test students though.
Andrew
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