Parameter Estimation of Kinetic Model

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Devak
Devak on 15 Apr 2014
Commented: Devak on 16 Apr 2014
I have a chemical kinetic model (2-Tissue compartment Model) with Constrained K3(where K3 is rate constant)
I have modelled plasma function along with Chemical kinetic model in order to plot the output characteristics(c_t)
I would like to estimate the Rate Constant k3 from the Code below
function c_t = output_function_constrainedK3(t, a1, a2, a3,b1,b2,b3,td, tmax,k1,k2,k3)
DV_free= k1/(k2+k3);
K3 = k3*((k1/k2)/DV_free);
K_1 = (k1*k2)/(k2+K3);
K_2 = (k1*K3)/(k2+K3);
c_t = zeros(size(t));
ind = (t > td) & (t < tmax);
c_t(ind)= conv(((t(ind) - td) ./ (tmax - td) * (a1 + a2 + a3)),(K_1*exp(-(k2+K3)*t(ind)+K_2)),'same');
ind = (t >= tmax);
c_t(ind)= conv((a1 * exp(-b1 * (t(ind) - tmax))+ a2 * exp(-b2 * (t(ind) - tmax))) + a3 * exp(-b3 * (t(ind) - tmax)),(K_1*exp(-(k2+K3)*t(ind)+K_2)),'same');
plot(t,c_t);
%plot(t,c_tnp);
axis([0 50 -2000 80000]);
xlabel time ;
ylabel concentration ;
end
The initial estimates for all the parameters is enlisted below
t=0:0.1:60;
td =0.3;
tmax=0.8;
a1=2501;
a2=18500;
a3=65000;
b1=0.5;
b2=0.7;
b3=0.3;
k1=0.014;
k2=0.051;
k3=0.07;
Kindly suggest me a method to estimate K3 parameter from nonlinear kinetic model code described above

Answers (1)

Arthur Goldsipe
Arthur Goldsipe on 16 Apr 2014
Here's an example that illustrates how to estimate parameters in a SimBiology model. This example was updated in R2014a to show how to use the new function sbiofit. If you have an earlier version of MATLAB, you can use sbioparamestim instead (as is reflected in the version of this example that shipped with your copy of MATLAB).
  1 Comment
Devak
Devak on 16 Apr 2014
Currently i am not using Simbiology tool box, is there any way in which i can estimate parameter K3 from the above function without using any toolbox

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