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Dear All,
Could anyone provide me equations to find values of Cssmax and Cssmin
after a oral dose. There is any free program that could do it.
Regards,
Daniel
[After one dose Cpmin = 0 ;-) Cpmax at tmax (=tpeak) from
http://www.boomer.org/c/p4/c08/c0803.html
At steady state Cpmin can be calculated from
http://www.boomer.org/c/p4/c15/c1503.html with various assumptions.
Cpmax can be estimated unless you integrate the multiple dose equation
(I haven't yet ...) or solve numerically searching for the tpeak at
steady state - db]
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Dear Daniel,
You wrote:
> Could anyone provide me equations to find values of Cssmax and Cssmin
> after a oral dose. There is any free program that could do it.
The equation for the concentration at steady state can be derived
directly
from the single dose equation:
C(t) = F * Dose / V * ka / (ka - k) * (exp(-k*t) - exp(-ka*t))
results in:
Css(t) = F * Dose / V * ka / (ka - k) * (exp(-k*t) / (1- exp(-k*tau)) -
exp(-ka*t) / (1 - exp(-ka*tau)))
at steady state with doses Dose at dosing interval tau.
Cminss is obtained by substituting t = 0 (or t = tau; this should give
the
same result).
The maximum concentration is reached if dC/dt = 0, thus:
dC/dt = F * Dose / V * ka / (ka - k) * (-k * exp(-k*t) / (1-
exp(-k*tau)) +
ka * exp(-ka*t) / (1 - exp(-ka*tau)))
From dC/dt = 0 it follows after replacing t with Tmax:
-k * exp(-k*Tmax) / (1- exp(-k*tau)) + ka * exp(-ka*Tmax) / (1 -
exp(-ka*tau)) = 0
which reduces to:
Tmax = ln(ka / k * (1- exp(-k*tau)) / (1 - exp(-ka*tau))) / (ka - k)
Substituting Tmax in Css(t) results in Cmaxss.
Please note:
- Tmax at steady state is different from (i.e. shorter than) Tmax after
a
single dose.
- these equation work for both ka > k and ka < k (not for ka = k).
Best regards,
Hans Proost
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
Email: j.h.proost.at.farm.rug.nl
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Copyright 1995-2010 David W. A. Bourne (david@boomer.org)