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I am trying to workout the equation for multiple oral dosing in a two
compartment model using the general principle:
(Cmax)n = (ka * F * Xo / V) * ((L * (1 - exp(-n * a * t)) / (1 -
exp(-a * t))) + (M * (1 - exp (-n * b * t)) / (1 -exp(-b * t))) - (N *
(1 - exp (-n * ka * t)) / (1 -exp(-ka * t))))
(Cmin)n = (ka * F * Xo / V) * ((L * (1 - exp(-n * a * t)) * exp(-a *
t) / (1 - exp(-a * t))) + (M * (1 - exp (-n * b * t)) * exp(-b * t)/ (1
-exp(-b * t))) - (N * (1 - exp (-n * ka * t)) * exp(-ka * t) / (1
-exp(-ka * t))))
However, upon inputting my values I noticed the max values are always
lower than the min values.
Does anybody have any comments or suggestions as to why this is the
Thanks in advance,
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The following message was posted to: PharmPK
There are some possible problems:
1) Your equation for Cmax does not give the maximum concentration, but
the concentration at the beginning of each dosing interval. For
intravenous dosing this is the maximum, but for extravascular dosing it
is not. Your finding that 'your Cmax' is lower than Cmin is correct,
since it is actually Cmin after the previous dose!
It is not so easy to calculate Cmax after extravascular dosing, since
one should know Tmax, which is dependent on all parameters including n.
2) It is not clear what your L, M and N refer to. If these are the
intercepts of the equation found by curve-fitting of a polyexponential
equation, the term
(ka * F * Xo / V)
should be left out.
3) The sum L + M + N should be equal to zero to satisfy the condition
that C=0 at time zero.
4) You are using N and n for different purposes; N is the intercept of
the ka-term, and n is the number of doses. This is confusing!
5) Note that t is the dosing interval, not time.
Johannes H. Proost
Dept. of Pharmacokinetics and Drug Delivery
University Centre for Pharmacy
Antonius Deusinglaan 1
9713 AV Groningen, The Netherlands
tel. 31-50 363 3292
fax 31-50 363 3247
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