Support:Documents:Examples:Estimate physiological parameters using a physiologically based model

Example of Implementation of the Physiologically Based Model

cm=compartmentModel;

% Define parameters
cm=addParameter(cm,'k1',0.1);
cm=addParameter(cm,'k2','k1/Fs');
cm=addParameter(cm,'k3','VG/(Fis*KGa+Fis*ECg*KGa/KGg)');
cm=addParameter(cm,'k4','VG/(Fic*KGa+Fic*ICg*KGa/KGg)');
cm=addParameter(cm,'k5','VH/(Fic*KHa+Fic*ICg*KHa/KHg)');

cm=addParameter(cm,'Fb',0.02);         % fraction of total space occupied by blood
cm=addParameter(cm,'Fis',0.3);          % fraction of total space occupied by interstitial space
cm=addParameter(cm,'Fic','1-Fis-Fb');  % fraction of total space occupied by intracellular space
cm=addParameter(cm,'F',1);

cm=addParameter(cm,'Pg',Pg);   % Plasma glucose concentration
cm=addParameter(cm,'ISg',5.4); % Interstitial glucose concentration
cm=addParameter(cm,'ICg',0.2); % Intracellular glucose concentration 

cm=addParameter(cm,'KGg',3.5); % Michaelis constant of glucose transporter (GLUT) for glucose
cm=addParameter(cm,'KHg',0.13; % Michaelis constant of hexokinase for glucose

cm=addParameter(cm,'KGa',3.5); % Michaelis constant of glucose transporter (GLUT) for glucose analog
cm=addParameter(cm,'KHa',0.13; % Michaelis constant of hexokinase for glucose analog

cm=addParameter(cm,'VG','(k1*Pg-k1*ISg)/(ISg/(KGg+ISg)-ICg/(KGg+ICg))'); % Maximal velocity of glucose transport for glucose=6FDG=2FDG
cm=addParameter(cm,'VH','(k1*Pg-k1*ISg)/(ICg/(KHg+ICg))'); % Maximal velocity of glucose phosphorylation for glucose=6FDG=2FDG

% Specific activity (sa): if the unit of image data is the same with that of input function, the specific activity is 1.
cm=addParameter(cm,'sa',1); 
% Usually, the decay time correction of image data is performed. So, dk is zero. 
cm=addParameter(cm,'dk',0);

% Define compartment
cm=addCompartment(cm,'IS'); % interstitial 
cm=addCompartment(cm,'IC'); % intracellular
cm=addCompartment(cm,'IP'); % intracellular phosphorylated 
cm=addCompartment(cm,'Junk');

% Define link
cm=addLink(cm,'L','Cp','IS','k1');
cm=addLink(cm,'K','IS','Junk','k2');
cm=addLink(cm,'K','IS','IC','k3');
cm=addLink(cm,'K','IC','IS','k4');
cm=addLink(cm,'K','IC','IP','k5');

% Define output of the first injection plus the second injection
wlistTotal={'IS','F';'IC','F;'IP','F'};
xlistTotal={'Ca','Fb'};
cm=addOutput(cm,'TissueTotal',wlistTotal,xlistTotal);

cm=addSensitivity(cm,'k1','ISg','ICg','Fis','Fb'); 

[PET,PETIndex,Output,OutputIndex]=solve(cm);