97
Appendix D
Programs for running the IRM
++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
function par = initparameters
global time_exp gluc_exp insul_exp A P InitialValues SecRate
%This program can be run by itself to simulate a single parameter set
%(A(28)=0) or be called by aFit.m (A(28)~=0).
%P="0", Tells the function of model equations "MMODEw_gut.m",
%that its is being called for a single simulation.
%===========================================================================
% Control parameters
%===========================================================================
Iglag=0; Res=.1;
A(30)=0; %Defines A(28), If A(28) not already defined, then it sets it equal to zero.
A(18)=0;%index used for counting number of returns to function.
%===========================================================================
%Length of time interval for Stand-alone run.
%===========================================================================
Minutes = 18;
%===========================================================================
%Parameters assumed to be constants
%FOR PARAMETER DEFINITIONS SEE TOP OF "MMODEw_gut.m".
%That is to find out that A(1)=p1.
%===========================================================================
A(1)=.6 ;A(3)=.001 ;A(5)=219.56 ;A(7)=1300;A(11)=.0001 ;A(14)=5.5;A(19)=75;
%===========================================================================
%Parameters not actually used:
%===========================================================================
A(20)=20; %for parabolic gluc input
%===========================================================================
%Parameters that probably vary
%===========================================================================
A(4)=.0008 ;A(8)=63;A(2)=84.2 ;
%===========================================================================
%Parameters used to describe or measure nature of the desease(diabetes)
%===========================================================================
A(6)=.0413 ;A(10)=7.7;A(12)=.0003 ;
%===========================================================================
%Set initial values from different data sets, load values from best run
%"A(27)=0" allows model to run with the pre-release compartment held constant
% ADDITIONAL LINE SET OFF BY %% ARE PARAMETER SETS OF UNKNOWN VALUE
%===========================================================================
%A(28)=0; %use if problems occur in clearing the global "A". (After crashes)
if A(28)==0;A(28)=1;P=0;
%For stand-alone run. A(28) must be set equal to the data set you wish to use
end;if A(28)==1;%This is Anderson' IVGTT data with Ig held constant
diabtezdataIVGTT;InitialValues=[y12(1,1) 1300 y12(2,1) 216 0];%ivgtt1
A(27)=0;A(3)=.0005 ;A(4)=4.4654;A(6)=.0855 ;A(9)=y12(2,1);A(12)=.0012;
end;if A(28)==2;%Sorensen's OGTT data, with Ig compartment held constant
diabtezdataOGTT;InitialValues=[y12(1,1) 1300 y12(2,1) 216 0];
A(27)=0;A(3)=.0006 ;A(4)=.0006;A(6)=.038 ;A(9)=y12(2,1);A(10)=6.13;
A(12)=.0002;
end;if A(28)==3;%This is an unknown data set for the IVGTT.
98
%not fit, will run with default values
tgi=LoadData;InitialValues=[tgi(1,2) 1300 tgi(1,3) 216 0];
end;if A(28)==4;%This is an unknown data set for the OGTT.
Data=getData;A(27)=0;InitialValues=[Data(2,1) 1300 Data(3,1) 216 0];
A(9)=y12(2,1);A(4)=.0003;A(6)=.036 ;A(9)=y12(2,1);A(10)=8;A(12)=.0006 ;
end;if A(28)==5;%This is Anderson' IVGTT data, Ig dynamic.
diabtezdataIVGTT;InitialValues=[y12(1,1) 850 7 216*1.2 0];
Iglag=.0001;A(17)=Iglag;
A(27)=1;A(1)=.5185 ;A(3)=.0032;A(4)=.0024;A(6)=.038 ;A(9)=8;A(10)=0;
A(12)=.0011 ;A(15)=0;A(20)=0;
end;if A(28)==6;%Sorensens OGTT1 data, Ig dynamic.
diabtezdataOGTT;InitialValues=[y12(1,1) 1300 y12(2,1) 216 0];
A(27)=1;A(3)=.0006 ;A(4)=.0006;A(6)=.038 ;A(9)=y12(2,1);A(10)=6.13;
A(12)=.0002
end;if A(28)==7;%Cobelli's OGTT data
CobelliDataOGTT;InitialValues=[Gluc_Ins(1,1) 1300 Gluc_Ins(2,1) 216 0];
A(27)=1;A(3)=.0019 ;A(4)=.0005;A(6)=.0135 ;A(9)=y12(2,1);A(10)=4.527;
A(12)=.0003 ;
end;
%===========================================================================
%the best previous parameter set for desired data is loaded in "A"
%If used as a guess for "aFit.m" the P=[the parameter numbers to be varied]
%The statement below puts those initial parameter values into "par"
%===========================================================================
if P~=0;for n=1:length(P);par(n)=A(P(n));end;end
%===========================================================================
%For stand-alone run of best parameter set
%===========================================================================
if P==0;ODErunNplot;%Call to "ODErunNplot.m"
SecRate=[0,0];A(28)=0;%reset global variables
End
++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
function v = MMODEw_Gut(t,y,par);%With New parameters
%global time_exp gluc_exp insul_exp A P SecRate
global A P SecRate
%===========================================================================
% If being used by aFitMM.m (P~=0), then set test parameter values
%===========================================================================
if P~=0;for n=1:length(P);A(P(n))=par(n);end;end
%===========================================================================
% set values for easy reading
%===========================================================================
G = y(1); Ig = y(2); Ip=y(3);Ir=y(4);
p1=A(1); h=A(2); p2=A(3); p3=A(4); IrTop=A(5);
S1=A(6); IgTop=A(7);Gb=A(8);Ib=A(9);food=A(10);
K1=A(11); K2=A(12);
Kabs=A(14);Iglag=A(17);A1=A(15);D_=A(19);ForMinutes=A(20);
%==========================================================================
%remove negative compartment values(Does not seem necessary)
%===========================================================================
%for indx=1:4;if y(indx)<0;y(indx)=0;end;end
%===========================================================================
% For using a delay, and running with dde23, no lag => no delay assumed
%===========================================================================
Z=y;%remove any lag, Z(1) is a current or a past glucose concentration
if t<Iglag;zz=A(8);end;if t>=Iglag;zz=Z(1);end;
99
%Yes is the heaviside function, gdiff is the pos reflection
Yes=(zz>h);
gdiff=Yes*(zz-h);
%===========================================================================
% If compartments Ig or Ir are full, then no more can be added
%===========================================================================
if Ig>A(7);p1=0;end;
if Ir>A(5);p2=0;end;
%must set v, and A(18) is the index on the matrix = number of returns
v = zeros(length(y),1);
A(18)=A(18)+1;
%===========================================================================
%When running stand alone (p=0), displays occasional time values.
%===========================================================================
if P==0;if A(18)/20==floor(A(18)/60); disp(t); end;end;
%===========================================================================
% Set transfer amounts.
%===========================================================================
Ir_in =Ig*p2*(IrTop>Ir) ; %Ir_in => from Ig and into Ir.
Ip_in =p3*Ir*gdiff; %Ip_in => from Ir and into Ip
%===========================================================================
% for parabolic glucose input. Simple test fitting
%===========================================================================
%inlag=8;meal=food*(t>inlag)*(t<ForMinutes+inlag)*(ForMinutes+inlag-t);
%===========================================================================
% Natucci's gut compartment. That is, oral glucose infusion from the gut.
% For IVGTT data set A(10)=food equal to zero
%===========================================================================
Ggut=y(5);
Rge = D_*(.014*1.23)*exp(-(.014*t)^1.23);meal = food*(Kabs*Ggut)/1.7 ;
dGgut = Rge - Kabs*Ggut;v(5)=dGgut;
%if A(20)>=5;meal=17*18*(t<ForMinutes)+(t>=ForMinutes)*3*18;end
%===========================================================================
% IRM (To hold Ig constant set A(27)=0, results in a three compartment model)
%===========================================================================
dG_dt = ((-S1*(G-Gb) - K1*Ip*G + meal));%Blood glucose concentration
dIg_dt = A(27)*((IgTop-Ig)*Yes*p1-Ir_in);%Pre-release insulin compartment
dIp_dt = Ip_in - K2*G*(Ip-Ib) ;
%Blood insulin concentration
dIr_dt = Ir_in - Ip_in ;
%Ready-to-release compartment
%===========================================================================
% v is function return vector
%===========================================================================
v(1) =dG_dt ; v(2)=dIg_dt ;v(3)=dIp_dt ; v(4)=dIr_dt ;
%===========================================================================
% Save insulin secretion rate values
%===========================================================================
SecRate(A(18),:)=[t,Ip_in + K2*G*Ib];
+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
%ODErunNplot.m
%
%Script. Runs the IRM and graphs it
%=====================================================================
options = odeset('RelTol',1e-5,'MaxStep',Res);
100
%function
time interval initial values options
[x ,y] = ode45('MMODEw_gut', [0, Minutes], InitialValues, options);x=x';y=y';
%=====================================================================
%Plots results
%=====================================================================
plotMelosh(x,y);%Call
++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
%plotMelosh: graphs the IRM
function v = plotMelosh(x,y);
global A SecRate P
%=====================================================================
%Choose the correct data set for evaluating the model's fit to the data
%=====================================================================
if A(28)==1;diabtezdataIVGTT;y12(3,:)=y12(2,:);y12(2,:)=y12(1,:);end;
if A(28)==2;diabtezdataOGTT;y12(3,:)=y12(2,:);y12(2,:)=y12(1,:);end;
if A(28)==3;tgi=LoadData;x12=tgi(:,1);y12(2,:)=tgi(:,2)';y12(3,:)=tgi(:,3)';end;
if A(28)==4;tgi=getData;x12=tgi(1,:);y12(2,:)=tgi(2,:);y12(3,:)=tgi(3,:);end;
if A(28)==5;diabtezdataIVGTT;y12(3,:)=y12(2,:);y12(2,:)=y12(1,:);end;
if A(28)==6;diabtezdataOGTT;y12(3,:)=y12(2,:);y12(2,:)=y12(1,:);end;
if A(28)==7;CobelliDataOGTT;y12(3,:)=Gluc_Ins(2,:);y12(2,:)=Gluc_Ins(1,:);
x12=Time;end;
Igran=y(2,:);Iplasma=y(3,:);
%=====================================================================
%Plots all compartments and the secretion rate.
%=====================================================================
figure(1);plot(x,y(1,:),'b-',x12,y12(2,:),'r--');
title('Blood Glucose Concentration, red is data');
figure(2);plot(x,Igran);title('Pre-release insulin');
figure(3);plot(x,Iplasma,'b-',x12,y12(3,:),'r--');
title('Blood Insulin Concentration, red is data');
figure(4);plot(x,y(4,:),'b-');title('Ready-to-release Insulin');
figure(5);plot(x,y(5,:)); xlabel('time (min)');
ylabel('Glucose in Gut (uU/ml)');
legend('model data', 'model simulation');
if P==0;
figure(6);plot(SecRate(:,1),SecRate(:,2));
title('Insulin Secretion Rate');axis([0 65 0 150]);
end
%EvaluateCloseness(x,y);%%Call
%=======================================================================
% Clear global variables=
%=======================================================================
if P==0;
A=0;time_exp=0;gluc_exp=0;insul_exp=0;InitialValues=0;SecRate=[0,0];
end
101
Appendix E
Programs for running the IPM (Overgaard’s and proposed)
++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
function par = initparameters
global time_exp InsSec_exp A P InitialValues GStep SecRate
%This program can be run by itself to simulate a single parameter set
%(A(28)=0) or be called by aFit.m (A(28)~=0).
%P="0", Tells the function of the IPM model equations "RMM.m",
%that its is being called for a single simulation.
%===========================================================================
% Control parameters
%===========================================================================
Iglag=0; Res=.1;
A(40)=0; %Defines A(28)---->
% If A(28) not already defined,then it sets it equal to zero.
A(10)=1;%index used for counting number of returns to function.
%===========================================================================
%Length of time interval for Stand-alone run.
%===========================================================================
Minutes = 180;
SecRate=[0,0];
%===========================================================================
%Set initial parameter values using Rune Overgaard's estimated parameter set
% then stores in values the global variable A
%===========================================================================
%
Kpeak Ksteady
t2=6; t3=60; p2=7; gama=.038; gstar=12.5; G=7.5; Kp=240; Ks=25;Gmax=20;Gmin=5;
p1=gama*gstar*t3*1;p3=1/(gstar*t3);p3b=p3*100;p4=1/t2;p5=Ks;Gstart=.1;GInt=50;
Ig0=0;
A(1)=p1; A(2)=p2; A(3)=p3; A(4)=p4; A(5)=p5;
A(6)=p3b;A(9)=Gmin; A(10)=0;
A(11)=Ig0;A(12)=Kp;A(13)=Ks;
A(18)=Gstart;A(19)=GInt;A(20)=Gmax;
InitialValues=[ A(11) A(12) A(13) ];
A(7)=100;A(8)=10;%Parameters created as a conversion factors from the data to
%that of the similation
%===========================================================================
%Options: A(27)=2=>RMM_2_compartment, A(27)=3=> RMM_3_compartment
%For the 2 comnpartment ignore the Ir graph
%===========================================================================
A(27)=3;
Minutes = 60; Res=.1;
Iglag=.000001;%used for dde23
%===========================================================================
%Set initial values from different data sets, load parameter values from
%best run. A used to transfer global parameter values
%===========================================================================
%A(28)=0; %use if problems occur in clearing the global "A". (After crashes)
if A(28)==0;A(28)=2;P=1;
%For stand-alone run. A(28) must = data set # that you wish to fit.
end;if A(28)==1;% Fit to StraubDataFig2;
102
A(1)=45.8*8;A(3)=p3*4;A(4)=p4; A(6)=p3b;A(7)=1;A(8)=1;A(9)=3;A(11)=000;
A(12)=185;A(13)=Ks;A(18)=16;A(19)=38;A(20)=16.7;%figure 4.3.2
InitialValues=[ A(11) A(12) A(13) ];
end;if A(28)==2;% Fit to BratanovaDataFig2;;
A(1)=45.8;A(9)=3;A(11)=4600;A(12)=139;A(13)=Ks;A(18)=8;A(19)=50;A(20)=15;
A(7)=1;A(8)=1;A(18)=7;A(19)=30;%figure Anulo_graph
InitialValues=[ A(11) A(12) A(13) ];
end;if A(28)==3;% Fit to AnullosDataFig3A;
A(1)=45.8;A(7)=1;A(8)=1;A(9)=3;A(11)=4600;A(12)=143;A(13)=Ks;A(18)=8;
A(19)=50;A(20)=15;A(7)=100;A(8)=10;A(18)=4.6;A(19)=30;%figure Anulo_graph
InitialValues=[ A(11) A(12) A(13) ];
end;if A(28)==4;% **NOT Done, Fit to BratanovaDataFig4;
%A(1)=p1; A(2)=p2; A(3)=p3; A(4)=p4; A(5)=p5; A(6)=p3b; A(9)=2; A(10)=0;
%A(11)=1300;A(12)=219;A(13)=Ks;A(18)=1;A(19)=59;A(20)=30;A(7)=.1;A(8)=10;
InitialValues=[ A(11) A(12) A(13) ];
end;if A(28)==5;%**NOT Done, Fit to BratanovaDataFig5;
%A(1)=p1; A(2)=p2; A(3)=p3; A(4)=p4; A(5)=p5;A(6)=p3b; A(6)=p3b; A(9)=Gmin;
%A(10)=0;A(11)=Ig0;A(12)=Kp;A(13)=Ks;A(18)=Gstart;A(19)=GInt;A(20)=Gmax;
InitialValues=[ A(11) A(12) A(13) ];
%-------------------------------------------%A(28)>6 fits the new proposed IPM to data
%The following parameter sets, are fit using
%the porposed IPM equarions.
%-------------------------------------------end;;if A(28)==6;% Fit to AnullosDataFig3A;
A(1)=45.8;A(3)=p3*8;A(6)=p3b;A(7)=1;A(8)=1;A(9)=3;A(11)=4600;A(12)=140;
A(13)=Ks;A(15)=0;A(18)=5;A(19)=28;A(20)=15;A(31)=150;A(32)=4600;
InitialValues=[ A(11) A(12) A(13) ];
end;;if A(28)==7;% Fit to StraubDataFig2
A(1)=.458;A(3)=p3*1.5;A(4)=p4; A(6)=p3b/2;A(7)=1;A(8)=1;A(9)=3;
A(11)=0;A(12)=190;A(13)=.1*Ks;A(18)=16;A(19)=50;A(20)=17;A(31)=150;A(32)=46000;
InitialValues=[ A(11) A(12) A(13) ];%figure 4.3.2
end;;if A(28)==8;%BratanovaFigure 5
A(1)=45.8*.01;A(3)=p3*.5;A(4)=p4; A(6)=p3b/6;A(7)=3;A(8)=-10;A(9)=2;
A(11)=4000;A(12)=100;A(13)=Ks;A(18)=9;A(19)=5;A(20)=30;A(31)=150;A(32)=4600;
InitialValues=[ A(11) A(12) A(13) ];
end;
%===========================================================================
%If P~=0 or 1, then P=[parameter numbers to be varied] and this program is
%being called by "aFit.m"
%===========================================================================
if P~=0;if P~=1;
for n=1:length(P);
par(n)=A(P(n));
end;end;
end;
%===========================================================================
%Run the numerical solver (if run as a stand-alone program)
%===========================================================================
if P==1;% Conditional A
options = odeset('RelTol',1e-5,'MaxStep',Res);
[t, y] = ode23('RMM',[0 Minutes],InitialValues,options) ;%Call RMM.m = IPM
%===========================================================================
%Prepare for graphing (if run as a stand-alone program)
%===========================================================================
y=y'; Ig = y(1,:); Ir=y(2,:); Ip=y(3,:);
%===========================================================================
%Choose data for secretion rate graph
103
%===========================================================================
if A(28)==1;StraubDataFig2;InsSec=A(7)*InsSec+A(8);tgi=[Time;InsSec]';end;
if A(28)==2;BratanovaDataFig2;InsSec=A(7)*InsSec+A(8);tgi=[Time;InsSec]';end;
if A(28)==3;AnullosDataFig3A;tgi=[Time;InsSec]';end;
if A(28)==4;BratanovaDataFig4;InsSec=A(7)*InsSec+A(8);tgi=[Time;InsSec]';end;
if A(28)==5;BratanovaDataFig5;InsSec=A(7)*InsSec+A(8);tgi=[Time;InsSec]';end;
if A(28)==6;AnullosDataFig3A;InsSec=A(7)*InsSec+A(8);tgi=[Time;InsSec]';end;
if A(28)==7;StraubDataFig2;InsSec=A(7)*InsSec+A(8);tgi=[Time;InsSec]';end;
if A(28)==8;BratanovaDataFig5;InsSec=A(7)*InsSec+A(8);tgi=[Time;InsSec]';end;
%----------------------------------------figure(1);plot(t,y(1,:),'b-');xlabel('time');ylabel('I_g','Rotation',0.0);
title('prerelease-granular insulin');
figure(2);plot(t,y(2,:),'b-');xlabel('time');ylabel('I_r','Rotation',0.0);
title('ready to release insulin');
figure(3);plot(t,y(3,:),'b-');xlabel('time');ylabel('I_p','Rotation',0.0);
title('blood insulin conc');
figure(4);plot(SecRate(:,1),SecRate(:,2),'b-',Time,InsSec,'r-');xlabel('time');
ylabel('ISR','Rotation',0.0);title('insulin secretion rate');
%----------------------------------------%garph combined plots
%----------------------------------------A(29)=2;
if A(29)==3
figure(5);
subplot(2,2,1);plot(t,y(1,:),'b-');xlabel('time');ylabel('I_g','Rotation',0.0);
title('prerelease-granular insulin');
subplot(2,2,2);plot(t,y(2,:),'b-');xlabel('time');ylabel('I_r','Rotation',0.0);
title('ready to release insulin');
subplot(2,2,3);plot(t,y(3,:),'b-');xlabel('time');ylabel('I_p','Rotation',0.0);
title('blood insulin conc');
subplot(2,2,4);plot(t,ISR,'b-');xlabel('time');ylabel('ISR','Rotation',0.0);
title('insulin secretion rate');
end
%===========================================================================
%Clear global variables (if run as a stand-alone program)
%===========================================================================
SecRate=[0,0];A=0;
end;% Conditional A
++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
function v = RMM(t,y,par);;
global A P SecRate;
%===========================================================================
% If being used by aFitMM.m (P~=0), then set test parameter values
%===========================================================================
if P~=0;if P~=1;for n=1:length(P);A(P(n))=par(n);end;end;end;
%===========================================================================
%For monitoring progress, counting returns, displaying time.
%===========================================================================
A(10)=A(10)+1;p=A(10);
%if (p-1)/100==floor((p-1)/100); disp(t); end;
%===========================================================================
%Covnvert global values for easy reading
%===========================================================================
Ig = y(1); Ir=y(2); Ip=y(3);
p1=A(1); p2=A(2); p3=A(3); p4=A(4); p5=A(5);p3b=A(6);Gmin=A(9);A15=A(15);
GStart=A(18);GInt=A(19);Gmax=A(20);IrTop=A(31);IgTop=A(32);
104
%===========================================================================
%Determine the glucose concentration, Glucose step, desired.
%===========================================================================
gluc_step
%===========================================================================
%Prepare for differential equation
%===========================================================================
v = zeros(length(y),1);
Yes=G>p2;
gdiff=Yes*(G-p2);
%===========================================================================
% Choose Overgaard's IPM (A(28) < 6)or the propsed IPM (A(28) >= 6)
%===========================================================================
if A(28)<6;
%Overgaard's IPM
Ir_in = p3*gdiff*Ig;
Ip_in = p3b*gdiff*Ir;
dIg_dt = Yes*p1 - Ir_in; %Pre-release insulin compartment
dIr_dt = Ir_in - Ip_in; %Ready-to-release insulin compartment
dIp_dt = Ip_in - p4*(Ip-p5);
end;
if A(28)>=6;
%Proposed IPM
Ir_in =Ig*p3*(IrTop>Ir); %Ir_in => from Ig and into Ir.
Ip_in =p3b*Ir*gdiff;
dIg_dt = (IgTop-Ig)*Yes*p1 - Ir_in ; %Pre-release insulin compartment
dIr_dt = Ir_in - Ip_in ; %Ready-to-release insulin compartment
dIp_dt = Ip_in - p4*(Ip-p5) ;
end;
%return v
v(1)=dIg_dt; v(2)=dIr_dt;v(3)=dIp_dt;SecRate(A(10),:)=[t,Ip_in + p4*p5];
++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
%gluc_step ISR
if t<=GStart;G=Gmin;;end;
if t>GStart;G=Gmax;;end;
if t>=GStart+GInt;G=Gmin;;end;
%For repeated glucose steps
if A(28)==8;% the only data that has repeated glucose steps
Gstart2=30;
if t>=Gstart2;G=Gmax;;end;
if t>Gstart2+ GInt;G=Gmin;;end;
end
105
Appendix F
Programs for fitting a system to clinical data
++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
function EXpar = aFitMM
global time_exp gluc_exp insul_exp A P InitialValues
close all;
%===================================================================================
% Choose output options, parameters to be varied, and the data set to be fit.
%===================================================================================
%Show graph updates during process, 0=>no then it runs faster
Graph=0;A(29)=Graph;%(Used in MMFunct line 38)
% choose parameters to be varied (by parmeter index in global variable A)
P=[4 11 12];
%Choose the data set to be fit
%1=>OGTT(IVGTT-Anderson), 2=>OGTT(OGTT-Sorrensen), 3=> OGTT("Load data"),4=>OGTT("getData")
%5=>NBRM(IVGTT-Anderson),6=>add Ig compartment+OGTT sorensen, 7=>Ig + OGTT cobelli's data
A(28)=5;
%===================================================================================
%Load data set chosen above
%time (minutes) glucose level (mg/dl) insulin level (uU/ml)
%---------------------------------------------------------------------------------------if A(28)==1;diabtezdataIVGTT;tgi=[x12;y12]';end;
if A(28)==2;diabtezdataOGTT;tgi=[x12;y12]';end;%Sorensens data
if A(28)==3;tgi=LoadData;end;%Morris's data
if A(28)==4;Data=getData;tgi=Data';end;%data from unknow recorded source
if A(28)==5;diabtezdataIVGTT;tgi=[x12;y12]';end;%Anderson's data
if A(28)==6;diabtezdataOGTT;tgi=[x12;y12]';end;%Sorensens data
if A(28)==7;CobelliDataOGTT;tgi=[Time;Gluc_Ins]';end;%Sorensens data
time_exp = tgi(:,1);
gluc_exp = tgi(:,2);
insul_exp = tgi(:,3);
%===================================================================================
% Set optimizer options
%===================================================================================
opts = optimset('Display','iter','TolFun', 1e-4,...%'iter' default: 1e-4
'TolX',1e-5,...
%default: 1e-4
'MaxFunEvals' , [],...
%800 default:
'LevenbergMarquardt','on',... %default: on
'LargeScale','on');
%default: on
lb = [];
ub = [];
%===================================================================================
% Apply optimizer (Returns optimal parameter set "EXpar")
%===================================================================================
Guess = initparameters;%Call
[EXpar,J,RESIDUAL,exitflag,OUTPUT,LAMBDA,Jacobian]=mylsqnonlin(@MMFunc,Guess,lb,ub,opts);
%Call
%===================================================================================
% Evaluate solution with optimal parameters (Runs numerical solver with "EXpar")
%===================================================================================
options = [];[t,x] = ode45(@MMODEw_gut,time_exp,InitialValues,options,EXpar);
plotMelosh(t',x');%Call
%===================================================================================
106
% Output optimized parameter values
%===================================================================================
%values=A % If used this line will display entire array of values for parameters and constants
for n=1:length(P);A(P(n))=EXpar(n);Disp=[P(n),EXpar(n)] ;end
%Will display only new optimized parameter values
%===================================================================================
% Clear global variables
%---------------------------------------------------------------------------------------A=0;P=0;time_exp=0; gluc_exp=0; insul_exp=0;InitialValues=0;SecRate=[0,0];
++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
function D = MMFunc(par)
global time_exp gluc_exp insul_exp A InitialValues
%This function called by "mylsqnonlin(@MMFunc,Guess,lb,ub,opts);" in
% aFit.m returns the residual values when model simulation is compared
% to a clinical data set. "mylsqnonlin.m" not included in the appendix
% since it is an unaltered matlab tool box program.
%===========================================================================
% Weighting scheme
%===========================================================================
w1 = 10*ones(size(gluc_exp)); %relative weights for glucose data
%w1(1:4) = [10 25 25 25 ];
%w1(15:size(gluc_exp))=10;%sensor first 2 samples
w2 = 10*ones(size(insul_exp)); %relative weights for insulin data
%w2(1:12) = [10 40 50 50 50 50 50 40 25 25 25 25 ]; %omit from criterion
w = [w1; w2];
%===========================================================================
% Run model with test values
%===========================================================================
options = [];
[t,y] = ode45(@MMODEw_gut,time_exp,InitialValues,options,par);%Call
%===========================================================================
% Measure + weigh residuals
%===========================================================================
%The following avoids crashes caused by dde23 when data vectors don't match up,
%results in throwing out the set of parameter values.
if length(y(:,1))==length(gluc_exp);%A
if length(gluc_exp)==length(y(:,3));%B
glucdif = y(:,1)-gluc_exp;
insudif = y(:,3)-insul_exp;
D = [glucdif; insudif];
D = w.*D;
%===========================================================================
% Show update
%===========================================================================
if A(29)==1;
%C show update during estimation process
N=length(time_exp);
set(gcf,'doublebuffer','on');
figure(2);
subplot(2,1,1);
plot(time_exp(1:N),y(1:N,1),'b',time_exp(1:N),gluc_exp(1:N),'or');
107
xlabel('time (min)');ylabel('glucose (mg/dl)');
legend('model simulation', 'model data'); drawnow;
subplot(2,1,2);
plot(time_exp(1:N),y(1:N,3),'b',time_exp(1:N),insul_exp(1:N),'or');
xlabel('time (min)');ylabel('insulin (uU/ml)');
legend('model simulation', 'model data'); drawnow;
end;end;end;%all conditionals: A,B, C ended.
%The following avoids crashes caused by dde23 when data vectors don't match up,
% results in throwing out the set of parameter values.
if length(y(:,1))~=length(gluc_exp)
for n=1:length(gluc_exp);y(n,1)=10000*n;y(n,2)=1000000*n;end
D=[1000000,1000000];
end
108
Appendix G
Programs for Clinical Data Sets
Clinical Data for Diabetes Tests: IVGTT, OGTT
++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
%diabtezdataIVGTT
% [Anderson] units: gluc=>mg/ml, insulin=>mu/dl
x12=[ 2.5 4 5 10 12 13 15 20 22.5 27.5 31 40 51 61 71 80 90 102 123 140 160 175];
y12=[350 283 250 217 212 205 195 192 173 165 140 125 103 89 82 75 70 70 70 71 80 87.5
25 132 85 50 49 42 40 30 30 26 29 20 13 13 11 10 7 10 6.5 7.5 7.5 6.5];
x12=x12-2.5;
++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
%diabtezdataOGTT
file "Hipzer master thesis Sorensen"(a web shortcut in favorites/thesis) units: gluc=>mg/ml, insulin=>mu/dl
x112=[60 70 080 088 100 110 119 130 138 148 158 168 178 188 197 206 216 227 237 246 256 267 278 286 295];
y12 =[80 88 109 122 123 118 113 105 099 093 091 090 085 082 080 084 076 070 066 064 061 061 061 061 063;
18 30 069 087 095 096 098 096 091 085 080 078 072 068 060 053 048 041 036 031 027 024 021 019 017];
for n=1:length(x112);x12(n)=x112(n)-60;end
%for n=3:4; y12(n,:)=y12(2,:);end;
++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
function tgi = LoadData
tgi = [ 0 92 11
2 350 26
4 287 130
6 251 85
8 240 51
10 216 49
12 211 45
14 205 41
16 196 35
19 192 30
22 172 30
27 163 27
32 142 30
42 124 22
52 105 15
62 92 15
72 84 11
82 77 10
92 82 8
102 81 11
122 82 7
142 82 8
162 85 8
182 90 7];
++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
%getData
%data Data3x21(t;G;I);
function Data=getData()%from file "OGTT4 has data not printed.pdf" units: gluc=> mmol/L, insulin=>pmol/L
Data=[
000 05 10 15 20 030 040 050 060 075 090 120 150 180 210 240 260 280 300 360 420;
49 49 51 61 75 88 88 84.5 78 71.5 68 58 51 49 48 49 49 49 49 49 48;
109
20 36 60 158 280 445 330 270 280 230 230 140 115 70 50 54 45 41 40 24 20 ];
for m=1:21;Data(2,m)=18*Data(2,m)/10;Data(3,m)=Data(3,m)/6;end
++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
Clinical Data on insulin secretion
++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
%BratanovaDataFig2
%Insulin Secretion rate
%y = IRI[secretion by percent of content/min], x=time[minutes]
%y = 128*IRI[secretion by % of content /min] is the approximate granule release rate /min.,
Time= [0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30];
InsSec = [ .1 .1 .1 1.2 1.3 .5 .51 .5 .49 .52 .47 .49 .5 .52 .58 .51 ];
++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
%BratanovaDataFig4
%Insulin Secretion rate
%y = IRI[pg/chamber/min], x=time[minutes]
Time=
[ 0 4 9 15 20 25 30 35 40 45 50 55 60 65 70 75 80];
InsSec = 100*[11 57 30 29 28.5 28 27 26 25 24 23 22 21 15 10 10 09 ];
++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
%BratanovaDataFig5
%Insulin Secretion rate
%Note the 1st 5 min of data was removed averaged about 8
%y = IRI[pg/chamber/min], x=time[minutes]
Time=
[ 0 5 10 15 20 25 30 35 40 45 50];
InsSec = [ 6 6 22 7 05 05 20 8 5 05 4.8];
++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
%AnullosDataFig3A.m
%Insulin Secretion rate
%y = IRI[secretion by percent of content/min], x=time[minutes]
%y = 128*IRI[secretion by % of content /min] is the approximate granule release rate /min.,
Time= [ 0 3 4.6 7 10 13 16 18 20 23 25 28 30 33 35 38 40 43 45];
InsSec = [ 10 10 153 81 55 50 50 48 47 50 53 58 52 44 21 17 10 9 9.5];
++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
%StraubDataFig2
%Insulin Secretion rate
%y = IRI[secretion by percent of content/min], x=time[minutes]
%y = 128*IRI[secretion by % of content /min] is the approximate granule release rate /min.,
Time= 0:2:50;
%
12
20
30
40
50
InsSec = [ 3 3 3 3 3 3 3 45 205 108 50 80 98 105 130 150 168 186 204 222 240 258 285 302 300 308];
110
Appendix H
Local Definitions
In order to make the paper less wordy some concepts will be given words to
refer to them. Thus, the following definitions are used only in this project.
Driving terms:
A term in a differential equation which directs, pushes or drives to
equation to some value. It may do it directly or only in concert
with some other equations. In the second case it will be referred
to as global driving. Driving terms usually drive the equation to
basal values.
Basalizing term:
A driving term that drives its equation to basal value.
Data based function: A function written to create a continuous function that contains all
the data points, and is somehow smoothed in between the points.
There are different ways to do this, one way is to connect the
points by line segments creating a piecewise defined function
consisting of linear subfunctions (see subfunction below).
Subfunction:
A function that is a part of, or included in, a larger function.
Repeatability:
After running a simulation does a model reset by itself to an
equilibrium point such that, if challenged a second time, it can
respond in a way comparable to its response to the first challenge.
Equilibrium Point:
A point, or set of compartment values, which if entered as initial
values, will result in the compartments remaining constant.
Designed Equilibrium Point: Since driving terms drive, or push, an equation to a specific
value, it is possible to write the equations such that they all push to
a certain set of compartment values, called a point. If that point is
intended to be an equilibrium point then it will be referred to as
the designed equilibrium point. It may not actually be an
equilibrium point at all.
111
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