Parameter Estimation of Kinetic Model

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

Answer 1

[Arthur Goldsipe]

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).

[Devak]

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