Matematisk Model for Mavesækkens Tømning - Danmarks Tekniske ...

18
106 MATLAB kode til simulering af forsøgsscenarie
19 % ========================================================================
20 % Modified 23.07.2009 SW
21 % ========================================================================
22 if nargin < 4
23 xinit = [0 0 55.9483 23.3399 5.7626 0.0295 0.0047 0.2997 −0 0]';
24 end
25 x = fsolve(@WrapHovorkaModel2Pancreas,xinit,[],u,ug,d,par);
26 xss = abs(x);
27 Gss = xss(3,1)/par.VG;
28 Iss = xss(5,1);
Listing D.4: WrapHovorkaModel2Pancreas.m
1 function xdot = WrapHovorkaModel2Pancreas(x,u,ug,d,par)
2 %WRAPHOVORKAMODEL The Hovorka model for the glucoregulatory system
3 %
4 % The function implements the Hovorka model for the gluco−regulatory system
5 % including absorption of food and iv administration of short−acting
6 % insulin together with Cobelli model for endogeneous insulin production.
7 %
8 % The model is in the form
9 %
10 % xdot(t) = (dx/dt)(t) = f(x(t),u,ug,d,par)
11 %
12 % with
13 %
14 % time : t [min]
15 % States: x = [D1; D2; S1; S2; Q1; Q2; I; x1; x2; x3; Ipo; Y]
16 % D1: Glucose compartment 1 in stomach/gut [mmol]
17 % D2: Glucose compartment 2 in stomach/gut [mmol]
18 % S1: Insulin compartment 1 SC layer [mU]
19 % S2: Insulin compartment 2 SC layer [mU]
20 % Q1: Plasma glucose (measurable) [mmol]
21 % Q2: Adipose glucose (non−measurable) [mmol]
22 % I : Plasma insulin [mU/L]
23 % x1: Insulin action on distribution/transport Q1−>Q2
24 % x2: Insulin action utilization in cells
25 % x3: Insulin action on EGP.
26 % Ipo:Insulin in portal vein [pmol/kg]
27 % Y : [mU/min]
28 % MVs : u = intraveneous insulin injection [mU/min]
29 % : ug = intraveneous glucose injection [g/min]
30 % DVs : d = CHO consumption [g/min]
31 % Parameters: par = {k12; ka1; ka2; ke; tauD; tauS; AG; kb1; kb2; VI; VG;
32 % EGP0; F01; MwG; gamma; K; alpha; beta; Sb; Gss}
33 % (this is a struct).
34 %
35 % The parameters may be constructed using the function
36 % HovorkaParametersPancreas.
37 %
38 % Syntax: xdot = WrapHovorkaModel2Pancreas(x,u,ug,d,par)
39
40 % ========================================================================