- On 1 Oct 2004 at 10:44:10, "Daniel Rossi de Campos" (Daniel.Campos.-at-.anvisa.gov.br) sent the message

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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] - On 4 Oct 2004 at 09:33:21, "Hans Proost" (j.h.proost.-at-.farm.rug.nl) sent the message

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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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