How could I do simutanoues parameter fitting for two series experimental data and multiple datasets?

Hello,

I have sets of ODEs and want to fit them for 2 series expermental data simutanouesly.

Basic idea is just like:

ODEs:

dadt(1)=-ka*a(1)

dadt(2)=ka*a(1)-ke*a(2)-k23*a(2)+k32*a(3)

dadt(3)=k23*a(2)-k32*a(3)

I have experimental mean data for compartment 2 and 3. Since the different doses were given in compartment1. So I seperated them into different datasets but they should share the same ka,k3,k23,k32.

How should I write the ofv for this case? How should I do parameter optimization next by using fminsearch or other tools?

[Alex Sha]

Just confused about "Dose", "compartment" and "observation", do they correspond to a(1), a(2) and a(3) respectively in your ODE functions?

Answer 1

[Star Strider]

See: Parameter Estimation for a System of Differential Equations for guidance.

Answer 2

[Alex Sha]

Hi, post your data please, if possible

[Yu Zhuo]

Good morning,

Please see attached data. I tried to make things easier.

I attached one .csv file which contains 'Dataset', 'Time', 'Dose', 'compartment', 'observation' columns. There are 3 different numbers under 'Dataset' column. Time are time in hour. 'Dose' was given at different time points to compartment1. 'Compartment' seperated out different series of experimental data ('observation'), which corresponds to the ODEs I have written above. I have 2 series of observations which are shown under 'observation' column.

Please note that the time for dosing or for those 2 series of observations are different.

My problem is how to write ofv and do next parameter optimization. Thanks in advance!

[Yu Zhuo]

1) Since time points are different for observations in compartment 2 and 3, I am confused if it is approporiate to put NaN in the input matrix for fminsearch or other optimizer?

2) Since there are 3 datasets and different doses were given, I am also confused that how to define a function of dose? and let matlab know which input matrix is for which dataset?

Thanks in advance!