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Date:   Tue, 23 Jun 2009 06:52:04 -0700
Reply-To:   PeterHuang <peterhuang1981@GMAIL.COM>
Sender:   "SAS(r) Discussion" <SAS-L@LISTSERV.UGA.EDU>
From:   PeterHuang <peterhuang1981@GMAIL.COM>
Subject:   Re: SAS differential equations fitting problem
Comments:   To:
Content-Type:   text/plain; charset=ISO-8859-1

On Jun 22, 7:10 pm, Shankar <> wrote: > Is this glucose/insulin absorption model? what are X and l ? > > I think you would need an initial/steady-state condition for X; For G > and l, you already have data at t= 0, so they can be used as initial > conditions; > > at t=0, can you assume dG/dt = 0 ? i.e initially absorption rate is > 0; > > I suspect your model is incomplete, i,e. you might need another ODE > for l; > > Thanks, > Shankar

Hi, Shankar, Thanks for your comments. This is a Minimal Model for Glucose and Insulin Kinetics .G(t) is the plasma glucose concentration at time t, I (t) is the plasma insulin concentration at time t, and X(t) is the interstitial insulin at time t. I do have another ODE for I(t) from another model. I combined them together and SAS codes are following:

PROC MODEL DATA=sample maxiter=1000; PARMS p1 p2 p3 n 0.3 gamma .003349 h 89.50;/* MODEL PARAMETERS*/ bounds p1>0,p2>0,p3>0, 0<n<1, 0<gamma<0.005, h>0; DERT.G = -X*G+p1*(90-G);/* DEFINING THE EQUATION*/ DERT.X = -p2*X+p3*(I-7);/* DEFINING THE EQUATION*/ if G > h then DERT.I = -n*I+gamma*(G-h)*t;/* DEFINING THE EQUATION*/ else DERT.I = -n*I;/* DEFINING THE EQUATION*/ FIT I INITIAL=(I=11)/ TIME=t DYNAMIC; FIT G INITIAL=(G=92)/ TIME=t DYNAMIC; FIT X INITIAL=(X=0.001)/ TIME=t DYNAMIC; RUN; quit;

However, there are still some problems: (1) X(t) is unknown; (2) After I set rough values for X(t) according to its practical meaning, there exists converging issues and the fitted parameter values are not reasonable. If you have any more comments, please let me know.

Thanks, Peter

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