Extended Toft's model


I am trying to modify the demri_3.c program to build a new program for 3dNLfim that would use nonlinear least squares to fit the Extended Toft’s model into my inputs [Ct.nii (a 3D+time dataset with the measured concentration of gadolinium in the brain) and Cp.1D (a 1D file with one value per timepoint, which is my vascular input function) ] to calculate Ktrans, Vp, and Ve (or Kep instead of Ve).

I am having issues in understanding what 3dNLfim needs for this purpose. As alternative approach, I also tried to simplify the Extended Toft’s equation as much as possible to use it in 3dNLfim with ‘Expr2’, but I failed (I guess because the parameter Kep is inside the integral, so I cannot calculate the integral, unless I provide an initial estimate for Kep, which does not seem to be useful since I still want Kep to be estimated by the nonlinear least squares fitting procedure).

Do you have any suggestion?

Thank you very much,

It has been a very long time since we looked at that program, but we’re happy to help. The model we used was a 2-compartment, 3 parameter model. The Expr2 model option is probably too simple for that. The use of that model required some preprocessing to transform the data given optional relaxivity maps from dual flip angles, an input vascular time series (estimated from a sagittal sinus vein signal), the subject hematocrit level and some other vaguely remembered things right now. I can probably dig up the scripts and the presentations on this. The published paper was this one:



In any case, it will probably be too complicated to discuss in a message board post, so email either Rick or me to set up an online meeting to discuss.