Parameter Estimation of Kinetic model

问题

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

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);
figure

%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

In the above function the parameters values for a1, a2, a3,b1, b2 ,b3, td, tmax, k1, k2 will remain constant.

I would like to know how K3 value changes with change in time t value, for this i would like to initially estimate K3 at t interval t=0:0.1:60..

Any help greatly appreciated

来源：https://stackoverflow.com/questions/23091987/parameter-estimation-of-kinetic-model