Matematisk Model for Mavesækkens Tømning - Danmarks Tekniske ...
Matematisk Model for Mavesækkens Tømning - Danmarks Tekniske ... Matematisk Model for Mavesækkens Tømning - Danmarks Tekniske ...
102 MATLAB kode til simulering af forsøgsscenarie 19 par.ke = 0.138; % Insulin elimination rate [1/min] 20 par.tauD = 40.0; % CHO absorption time constant [min] 21 par.tauS = 55.0; % Insulin absorption time constant [min] 22 par.AG = 0.8; % CHO utilization [−] 23 24 SI1 = 51.2e−4; % Transport insulin sensitivity [L/mU] 25 SI2 = 8.2e−4; % Disposal insulin sensitivity [L/mU] 26 SI3 = 520e−4; % EGP insulin sensitivity [L/mU] 27 28 par.kb1 = par.ka1*SI1; % Activation rate [(L/mU)/min] 29 par.kb2 = par.ka2*SI2; % Activation rate [(L/mU)/min] 30 par.kb3 = par.ka3*SI3; % Activation rate [(L/mU)/min] 31 32 par.VI = 0.12*BodyMass; % Insulin distribution volume [L] 33 par.VG = 0.16*BodyMass; % Glucose distribution volume [L] 34 par.EGP0 = 0.0161*BodyMass; % Liver glucose production at zero insulin 35 % [mmol/min] 36 par.F01 = 0.0097*BodyMass; % Insulin independent glucose consumption 37 % [mmol/min] 38 39 par.MwG = 180.1577; % Molecular weight of glucose [g/mol] 40 41 % Parameters from Cobelli 42 norm = 1/6.00; % [mU/pmol] 43 44 par.gamma = 0.5; % Transfer rate constant between portal vein 45 % and liver [1/min] 46 par.K = (2.3*norm*par.MwG*0.1)*(BodyMass/par.VG); % [mU/mmol] 47 par.alpha = 0.05; % [1/min] 48 par.beta = 0.11*norm*0.1*par.MwG*BodyMass; % [(mU/min)/(mmol/L)] 49 50 HEb = 0.6; % [−] 51 m5 = 0.0304*(1/norm)*(1/BodyMass); % [min/mU] 52 m6 = 0.6471; % [−] 53 54 par.Sb = ((m6−HEb)/m5)*0.36; % [mU/min] 55 % For BW = 70 kg is par.Sb = ((m6−HEb)/m5)*0.36 and I(0) = 5.7677 56 % For BW = 60 kg is par.Sb = ((m6−HEb)/m5)*0.12 and I(0) = 5.7253 57 par.Gss = 4.9656; % [mmol/L] for BW = 70 kg Listing D.2: HovorkaModel2pancreas.m 1 function xdot = HovorkaModel2pancreas(t,x,u,ug,d,par) 2 %HOVORKAMODEL 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(t,x(t),u,ug,d,par) 11 % 12 % with
13 % 14 % time : t [min] 103 15 % States: x = [D1; D2; 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 % Q1: Plasma glucose (measurable) [mmol] 19 % Q2: Adipose glucose (non−measurable) [mmol] 20 % I : Plasma insulin [mU/L] 21 % x1: Insulin action on distribution/transport Q1−>Q2 22 % x2: Insulin action utilization in cells 23 % x3: Insulin action on EGP. 24 % Ipo:Insulin in portal vein [pmol/kg] 25 % Y : [mU/min] 26 % MVs : u = intraveneous insulin injection [mU/min] 27 % : ug = intraveneous glucose injection [g/min] 28 % DVs : d = CHO consumption [g/min] 29 % : Gss = Basal plasma glucose concentration [mmol/L] 30 % Parameters: par = {k12; ka1; ka2; ke; tauD; tauS; AG; kb1; kb2; VI; VG; 31 % EGP0; F01; MwG; gamma; K; alpha; beta; Sb; Gss} 32 % (this is a struct). 33 % 34 % The parameters may be constructed using the function 35 % HovorkaParametersPancreas. 36 % 37 % Syntax: xdot = HovorkaModel2pancreas(t,x,u,ug,d,par) 38 39 % ======================================================================== 40 % Modified 23.07.09 SW 41 % ======================================================================== 42 %% Extract variables 43 % Extract states 44 D1 = x(1,1); % Glucose compartment 1 in stomach/gut [mmol] 45 D2 = x(2,1); % Glucose compartment 2 in stomach/gut [mmol] 46 Q1 = x(3,1); % Plasma glucose (measurable) [mmol] 47 Q2 = x(4,1); % Adipose glucose (non−measurable) [mmol] 48 I = x(5,1); % Plasma insulin concentration [mU/L] 49 x1 = x(6,1); % Insulin action on distribution/transport [mU] 50 x2 = x(7,1); % Insulin action on disposal in adipose tissue [mU] 51 x3 = x(8,1); % Insulin action on EGP 52 53 Ipo = x(9,1); % Insulin mass in liver [mU] 54 Y = x(10,1); % Transfer of insulin [mU/min] 55 56 % Extract parameters 57 k12 = par.k12; % Transfer rate [1/min] 58 ka1 = par.ka1; % Deactivation rate [1/min] 59 ka2 = par.ka2; % Deactivation rate [1/min] 60 ka3 = par.ka3; % Deactivation rate [1/min] 61 ke = par.ke; % Insulin elimination rate [1/min] 62 tauD = par.tauD; % CHO absorption time constant [min] 63 tauS = par.tauS; % Insulin absorption time constant [min] 64 AG = par.AG; % CHO utilization [−] 65 kb1 = par.kb1; % Activation rate [(L/mU)/min] 66 kb2 = par.kb2; % Activation rate [(L/mU)/min] 67 kb3 = par.kb3; % Activation rate [(L/mU)/min]
- Page 65 and 66: 5.3 7 modeller for mavesækkens tø
- Page 67 and 68: 5.3 7 modeller for mavesækkens tø
- Page 69 and 70: 5.3 7 modeller for mavesækkens tø
- Page 71 and 72: 5.3 7 modeller for mavesækkens tø
- Page 73 and 74: 5.4 Sammenligning af de 7 modeller
- Page 75 and 76: 5.5 Resume af Kapitel 5 61 5.5 Resu
- Page 77 and 78: Kapitel 6 Simulering af forsøgssce
- Page 79 and 80: 6.1 Hovorka modellen 65 ˙Q1(t) = U
- Page 81 and 82: 6.2 Implementering af model for bug
- Page 83 and 84: 6.2 Implementering af model for bug
- Page 85 and 86: 6.3 Simulering af clamp-forsøg 71
- Page 87 and 88: 6.3 Simulering af clamp-forsøg 73
- Page 89 and 90: 6.3 Simulering af clamp-forsøg 75
- Page 91 and 92: 6.4 Diskussion af simulering af cla
- Page 93 and 94: 6.5 Resume af Kapitel 6 79 ducerer
- Page 95 and 96: Kapitel 7 Konklusion I dette bachel
- Page 97 and 98: Bilag A MATLAB kode til kantfinding
- Page 99 and 100: 79 xlabel('Time [min]','fontsize',1
- Page 101 and 102: 22 if Data(i,j) ≥ cs 23 if Data(i
- Page 103 and 104: Bilag B MATLAB kode til fit af data
- Page 105 and 106: 82 t = 0:1:400; 83 Q = (1 + K*(t/te
- Page 107 and 108: Bilag C MATLAB kode til behandling
- Page 109 and 110: 79 % Plot of the model of Y with da
- Page 111 and 112: 189 %%%%%%%%%%%%%%%%%%%%%%%%% 1 par
- Page 113 and 114: 299 print('−dpng', '−loose', ['
- Page 115: Bilag D MATLAB kode til simulering
- Page 119 and 120: 105 123 Q2dot = Q12 − Q21 − Q2o
- Page 121 and 122: 41 % Modified 23.07.09 SW 107 42 %
- Page 123 and 124: 109 81 subplot(223) 82 stairs(T,D,'
- Page 125 and 126: 90 91 % Plot of iv insulin infusion
- Page 127 and 128: 99 ylabel('Insulin infusion (mU/min
- Page 129 and 130: Bilag E Billeder fra forsøg med no
- Page 131 and 132: 117 Figur E.3: Her ses forsøgspers
- Page 133 and 134: Bilag F Formelle dokumenter i forbi
- Page 135 and 136: Komitéens reg.nr. (KF)____________
- Page 138 and 139: Formål Formålet med dette projekt
- Page 140 and 141: Forsøgsprocedure Efter forudgåend
- Page 142 and 143: Publikation Forsøgsresultaterne vi
- Page 144 and 145: Effekten af hypo-, normo- og hyperg
- Page 146 and 147: Driftsomkostninger og udgifter til
- Page 148 and 149: til at dosere indsprøjtningerne af
- Page 150 and 151: Følgende annonce indrykkes på int
- Page 152 and 153: 138 LITTERATUR [10] O. Goetze, A. S
- Page 154: 140 LITTERATUR [34] K. Vollmer, H.
13 %<br />
14 % time : t [min]<br />
103<br />
15 % States: x = [D1; D2; Q1; Q2; I; x1; x2; x3; Ipo; Y]<br />
16 % D1: Glucose compartment 1 in stomach/gut [mmol]<br />
17 % D2: Glucose compartment 2 in stomach/gut [mmol]<br />
18 % Q1: Plasma glucose (measurable) [mmol]<br />
19 % Q2: Adipose glucose (non−measurable) [mmol]<br />
20 % I : Plasma insulin [mU/L]<br />
21 % x1: Insulin action on distribution/transport Q1−>Q2<br />
22 % x2: Insulin action utilization in cells<br />
23 % x3: Insulin action on EGP.<br />
24 % Ipo:Insulin in portal vein [pmol/kg]<br />
25 % Y : [mU/min]<br />
26 % MVs : u = intraveneous insulin injection [mU/min]<br />
27 % : ug = intraveneous glucose injection [g/min]<br />
28 % DVs : d = CHO consumption [g/min]<br />
29 % : Gss = Basal plasma glucose concentration [mmol/L]<br />
30 % Parameters: par = {k12; ka1; ka2; ke; tauD; tauS; AG; kb1; kb2; VI; VG;<br />
31 % EGP0; F01; MwG; gamma; K; alpha; beta; Sb; Gss}<br />
32 % (this is a struct).<br />
33 %<br />
34 % The parameters may be constructed using the function<br />
35 % HovorkaParametersPancreas.<br />
36 %<br />
37 % Syntax: xdot = Hovorka<strong>Model</strong>2pancreas(t,x,u,ug,d,par)<br />
38<br />
39 % ========================================================================<br />
40 % Modified 23.07.09 SW<br />
41 % ========================================================================<br />
42 %% Extract variables<br />
43 % Extract states<br />
44 D1 = x(1,1); % Glucose compartment 1 in stomach/gut [mmol]<br />
45 D2 = x(2,1); % Glucose compartment 2 in stomach/gut [mmol]<br />
46 Q1 = x(3,1); % Plasma glucose (measurable) [mmol]<br />
47 Q2 = x(4,1); % Adipose glucose (non−measurable) [mmol]<br />
48 I = x(5,1); % Plasma insulin concentration [mU/L]<br />
49 x1 = x(6,1); % Insulin action on distribution/transport [mU]<br />
50 x2 = x(7,1); % Insulin action on disposal in adipose tissue [mU]<br />
51 x3 = x(8,1); % Insulin action on EGP<br />
52<br />
53 Ipo = x(9,1); % Insulin mass in liver [mU]<br />
54 Y = x(10,1); % Transfer of insulin [mU/min]<br />
55<br />
56 % Extract parameters<br />
57 k12 = par.k12; % Transfer rate [1/min]<br />
58 ka1 = par.ka1; % Deactivation rate [1/min]<br />
59 ka2 = par.ka2; % Deactivation rate [1/min]<br />
60 ka3 = par.ka3; % Deactivation rate [1/min]<br />
61 ke = par.ke; % Insulin elimination rate [1/min]<br />
62 tauD = par.tauD; % CHO absorption time constant [min]<br />
63 tauS = par.tauS; % Insulin absorption time constant [min]<br />
64 AG = par.AG; % CHO utilization [−]<br />
65 kb1 = par.kb1; % Activation rate [(L/mU)/min]<br />
66 kb2 = par.kb2; % Activation rate [(L/mU)/min]<br />
67 kb3 = par.kb3; % Activation rate [(L/mU)/min]
Change language