a) Implemented the new 2CXM\LLS model.
b)  Added a hypermater to optionally exclude the non-physiological voxels.
c)  Defect fixed: Enable FireVoxel document\file when there is an active model without hyperparameters.

2CXM model:  two variants were implemented -  NLLS and LLS

With LLS variant a double integration is performed and the corresponding 4x4 linear system is solved using SVD.  Resulting solution is converted to physiological parameters {vp,ve,PS,Fp} and substituted to an analytical solution containing a convolution of two different exponents with the AIF.

Sample ROI for the test

Tests were performed on the GRASP-4D with 76 timepoints [0,411] sec.

Small ROI (yellow was chosen)






First we performed the fitting with "ROI as a single TAC".












A good fit was observed RMSE=25.  But corresponding parameters contain the negative value, which is not physiological.

Next we performed voxel-by-voxel fitting.  This model   #45 2CXM-LLS  has a single hyperparameter "Exclude invalid", which optionally excludes the unphysiological voxels from the map (defaullt=0  - Include all).

LLS: Residual distribution [0,100] (include all mode)

 If we turn  "Exclude Invalid =1",  this would exclude the voxels from the result where one of the key fittted parameters   are negarive:  this includes transit times {T,Te,Tp}  and {vp,ve,PS}

Fitting with  unphysiological (invalid) voxels removed.

When such invalid voxels are removed, we can see that a minor portion of the ROI resulted in non-negative parameter values.




NLLS variant:  gridded Simplex algorithm was used.

Below is the fitting residual comparison for LLS and NLLS.

LLS:  fit residual distribution [0,100]

NLLS: fit residual distribution [0,100]

Timing:  for the whole slice ROI  (24,000 voxels):
Processing times  are   LLS:  0.5 sec
                                     NLLS:  55 sec