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Re: Steady state model

From: Sherwin K Sy <>
Date: Thu, 6 Aug 2009 11:20:26 -0400

Dear all,

I thank you very much for pointing me to the references that mention them
and also illustrating the solutions for SS equations. They are very helpful.

What's interesting also is that Monolix uses the summation of the individual
linearized solution to fit a multiple dose profile, rather than setting it
up as ODE and use something like a unit delta function to simulate an
injection multiplied by the dose. What are your experiences with this



On Thu, Aug 6, 2009 at 3:38 AM, AVG (Andreas Velsing Groth) <

> Hello Sherwin,
> SS=1 infers a perfect steady state situation, i.e. a particular dosing
> event has been occurring with a particular time interval for infinitely long
> - and nothing else is happening. For the "standard PK model library" in
> NONMEM, i.e. for those linear ODE systems with their analytical (closed
> form) solutions implemented in specific NONMEM Advans, the single dose (SD)
> solution is a sum of exponential terms e.g. for a 1st order absorption 1st
> order elimination 1-cmpt model the solution for conc in the central cmpt is
> C(t)= (exp(-K*t)-exp(-Ka*t)) *D*F*Ka/V/(Ka-K). Because all processes in
> these models are linear, when you add more doses their individual
> contributions to C(t) are additive. So for n doses interspaced by a constant
> interval tau, with the example model we get
> C(t)= (exp(-K*t)+exp(-K*(t+tau))+exp(-K*(t+2tau))...+exp(-K*(t+n*tau))
> -exp(-Ka*t)-exp(-Ka*(t+tau))-exp(-Ka*(t+2tau))...-exp(-Ka*(t+n*tau)))
> *D*F*Ka/V/(Ka-K).
> This is the sum of two geometric series multplied by a constant, which
> reduces to
> C(t)= (exp(-K*t)*(1-exp(-K*n*tau))/(1-exp(-K*tau))
> -exp(-Ka*t)*(1-exp(-Ka*n*tau))/(1-exp(-Ka*tau)) *D*F*Ka/V/(Ka-K).
> As n tends to infinity, 1-exp(-K*n*tau) and 1-exp(-Ka*n*tau) both tend to 1
> so for true steady state i.e. infinite n you get the simpler expressions
> referred by Samer.
> I believe the Gabrielsson & Weiner PKPD book has some of the SS solutions
> in it.
> Best,
> Andreas
> -----Original Message-----
> From: owner-nmusers
> On Behalf Of Mouksassi Mohamad-Samer
> Sent: 6. august 2009 08:23
> To: nmusers
> Cc: n.holford
> Subject: RE: [NMusers] Steady state model
> Hello Sherwin,
> All SS routines source code are located at the C:\nmvi\pr folder.
> Each Advan closed form model has specific routines (and equations for SS)
> that can be used with it.
> For linear models the magic factor for steady state computation will be:
> exp(-rate.constant.time)/(1-exp(-rate.constant.Tau).
> Monolix guide: Monolix31_PKPD_library.pdf has a lot of SS equations for
> commonly used models.
> Of course general Advans have their general SS routines too and as Nick
> mentioned there is some root finding going on:
> a comment from the SS6.FOR routine reads
> C 0=DADT(0)+DA*A+R
> C A=-DAINV*(DADT(0)+R)
> ...
> Happy Reading !
> Bests,
> Samer
> -----Original Message-----
> From: owner-nmusers
> Sent: Wed 8/5/2009 15:44
> To: nmusers
> Subject: Re: [NMusers] Steady state model
> Sherwin,
> I dont understand exactly how NONMEM computes the steady state value but
> with ODEs it seems to be done using a numerical root finding procedure i.e.
> solves for the amt in each of the compartments when all the DEs have a
> value of zero.
> The amt in each compartment is set to the steady state value. There is no
> initial 'parameter' for the compartment. Compartment amounts are variables.
> Parameters are constants. Parameters (e.g. THETA values) are used in the
> ODEs to define the DE values.
> Perhaps Alison Boechmann (who wrote the code) could give a more thorough
> answer?
> Nick
> Sherwin K Sy wrote:
> > Dear NONMEM users,
> >
> > I'm wondering what equation or ODE is used in NONMEM when the steady
> > state is set (i.e. SS = 1). Is it the case that the initial parameter
> > for the compartment is set to a different value? If so, how does
> > NONMEM set this value?
> >
> > I would appreciate if anyone can provide me with a reference or point
> > me to where I can find this information, including the type of
> > equation used for extravascular, iv bolus and iv infusion models.
> >
> > Thanks,
> >
> > Sherwin
> >
> >
> --
> Nick Holford, Professor Clinical Pharmacology Dept Pharmacology & Clinical
> Pharmacology University of Auckland, 85 Park Rd, Private Bag 92019,
> Auckland, New Zealand n.holford
> fax:+64(9)373-7090
> mobile: +64 21 46 23 53

Received on Thu Aug 06 2009 - 11:20:26 EDT

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