Matematisk Model for Mavesækkens Tømning - Danmarks Tekniske ...

105
123 Q2dot = Q12 − Q21 − Q2out; % Compartment 2 [mmol/min]
124
125 % =========================================================================
126 % Insulin subsystem
127 % =========================================================================
128 x1dot = −ka1*x1+kb1*I; % Insulin influence on transport/distubtion
129 x2dot = −ka2*x2+kb2*I; % Insulin influence on disposal in adipose tissue
130 x3dot = −ka3*x3+kb3*I; % Insulin influence on EGP in liver
131
132 % =========================================================================
133 % Insulin secretion
134 % =========================================================================
135 S = gamma*Ipo; % Insulin secretion [mU/min]
136
137 Idot = UI/VI − ke*I + S/VI; % Change in plasma insulin concentration
138 % [(mU/L)/min]
139
140 % Insulin uptake in portal vein
141 if Q1dot > 0
142 Spo = Y + Sb + K*Q1dot; % [mU/min]
143 else
144 Spo = Y + Sb; % [mU/min]
145 end
146 Ipodot = −S + Spo; % Change in insulin amount in portal vein [mU/min]
147
148 if beta*(G−Gss) ≥ −Sb
149 Ydot = −alpha*(Y − beta*(G−Gss)); % [(mU/min)/min]
150 else
151 Ydot = −alpha*(Y + Sb); % [(mU/min)/min]
152 end
153
154 %% Return derivatives
155 xdot = [D1dot; D2dot; Q1dot; Q2dot; Idot; x1dot; x2dot; x3dot; Ipodot;...
156 Ydot];
Listing D.3: HovorkaBasalState2Pancreas.m
1 function [Gss,Iss,xss] = HovorkaBasalState2Pancreas(u,ug,d,par,xinit)
2 % HOVORKABASALSTATE Computes the basal state of the Hovorka model
3 %
4 % The basal state is identical to the steady state. Given the inputs
5 %
6 % Syntax: [Gss,Iss,xss] = HovorkaBasalState2Pancreas(u,ug,d,par,xinit)
7 %
8 % Gss : [mmol/L] Basal plasma glucose concentration (steady state)
9 % Iss : [mU/L] Basal plasma insulin concentration (steady state)
10 % xss : Basal states in the Hovorka model (steady state)
11 %
12 % u : [mU/min] basal insulin injection
13 % ug : [g/min] basal glucose injection
14 % d : [g/min] basal oral food intake (usually zero)
15 % par : Parameters (see HovorkaParametersPancreas.m)
16 % xinit : initial guess on the basal states (optional)
17