Solve Compartmental Model with lsqcurvefitting

Hi,

My question is about the following convolution:

C(t) = Ca(t) x K1*exp(-k2*t)

where x is the convolution. I have the x- and y-values of the signals C(t) and Ca(t). With a least squares estimation, I want to estimate the parameters K1 and k2.

I started this with the function lsqcurvefitting, for which I first set up the following function, like the example in the help file

function F = myfun(x,xdata)
F = (x(1)*exp(x(2)*xdata));

But, the problem is that I have two sets of xdata and two sets of ydata (from C(t) and Ca(t)). Is this problem even possible to solve with the lsqcurvefitting? because if I want to solve this with the following code, it does not like the function at all (and that is because I totally skipped the convolution with Ca(t), but I don't know how to implement this).

   K0 = [0.02; 0]; % Starting guess  
   [K,resnorm] = lsqcurvefit(@myfun,K0,xdata,ydata)

Btw, the xdata and ydata mentioned in this script is from the C(t) dataset.

Hope this problem is clear to you. Thanks in advance :)

[Matt J]

Are the xdata uniformly spaced?

[Inge]

No, but the xdata for both C(t) and Ca(t)is spaced in the same, non-uniformly manner. This is the xdata:

 0     5    10    15    20    25    30    35    40    45    50    55    60    65    70    75    80    85    90    95   100   110   120   130   140   150   160   170   180   190   200   250   300   350   400   450 
500   550   600   695   790

Answer 1

[Matt J]

For a fixed k2, you should be able to do a numerical convolution using TRAPZ within your F(x,xdata) function.

Since your K1 function only affects the objective function linearly, you might also consider using

http://www.mathworks.com/matlabcentral/fileexchange/10093-fminspleas

instead of LSQCURVEFIT.