Liver DCDI model:  adding two implementations of this model to the UI. 
The "Standard" variant, has exact implementation of the Sourbron's paper with the addition of the Exam length parameter and the variables {TotalFlow,fa,Ve,ki}.
The "Experimental" variant hosts new investigations, such as independently derived "Ta" arterial delay time.

Fixed the defect in   "Roi>Convert 3D to 4D" function.  DICOM-style headers were not properly constructed for a newly created 4D entity.

URAL registration 3D/4D:   in case when non-textured URAL measure is selected, applied very efficient gradient interpolation technique that result in a significant speed up during the AutoFocus and especially the Finetune stage.

Completely re-engineered the image gradient field reslicing function.

Registration 4D:   Eliminated an excessive temporary memory allocation during the 4D registration.  This was the cause of the memory allocation failure during the registration of large 4D datasets.

Latest DCDI approach to  Arterial (Ta) and Venous (Tv) delay approach   was tested:

Arterial delay is defined graphically (at the moment) by analyzing the AIF and  roiTAC.
(blue-AIF,  red-VIF, green-roiTAC)

Define:   Ta = ContrastArrivalTimeROI - ContrastArrivalAIF.
For this specific ROI it was Ta = 16 sec.
At the moment User punches in this time delay, but will be entirely automatic later.

Then we perform 5 parameter fitting of DCDI model  {TotalFlow,fa,Ki,Ve,Tv}.  We set  Tv=[0,8] seconds.

Result is encouraging, with fa=0.33.  (Blue is the data curve, black is the Model curve)

ROI was made very small to avoid the blood vessels.

Time to Peak  (in seconds) parametric map for the liver  , case YL.
Vein network shows varying arrival times.  There seem to be a substantial delay between the main Portal Vein (where we sample VIF) and the peripheral (?) branches (which actually supply the tissue).
Delays seem to be upto 15 seconds.

Liver DCDI:  Based on the discussion with Dr. Rusinek, experimenting with the alternative ways to calculate the Arterial fraction and then substitute it into the Sourbron's equation for fitting.  Reminds me of "Segmented fit" in IVIM promoted by Eric Sigmund.

Stress testing correctness of the fitting procedure, substituting  AIF and VIF (in 2 separate experiments) as the Data curve and comparing to the analytically derived result.

Assembled {AIF,VIF,+6 ROI Tacs} package for the external verification of Liver DCDI model fitting.

Adding the allowed ranges of parameters {Fa,Fv,Ve,Ki} for Liver DCDI model, so the User\Researcher could control those parameters directly for investigations.

Provided to Hersh the full analysis \report on 3 cases   {KA,LP,YL} with the respect to Liver DCDI model.

Analysis of DCDI cases  ("Good": 1-KA, 2-LP,  "Bad":  3-YL

Liver DCDI model:  Obtained a very good fit, with all parameter values are now in the allowd physiological ranges.  However, the question remains why the Arterial Fraction is essentially a 0?  Does it have an explanation?
ROI to model, was made very small with the effort to exclude possible blood vessels.

Rewriting the Liver DCDI fit procedure, so the Amoeba optimization is performed many times from various starts in the grid, instead of a single start.

Implemented variant of Amoeba-local optimization that is guaranteed to stay within User-specified parameter bounds.  Applied it to the problematic liver case from Hersh. However, the obtained fit is not as good as for other cases, so continue the work on more efficient optimization procedure.  Here is current best result:

Further investigation of the fitting problems on Hersh's example:  very good fit is found by Amoeba,  but the best value is found is outside the acceptable physical range of parameters (f.e. the Arterial fraction is negative).  So clearly the Optimization procedure has to change in some way.  Investigations to continue.

Investigating and fixing what most likely a defect in the fitting of the DCDI model.  Issue is that two curves below, one with obviously worse fit is presently returned with the smaller residual.

Further optimized the search of the required precision of variables before Amoeba optimization.  This is relevant to all optimizations using Amoeba.  It was initiated in the context of Liver registration which was sped up by another 5%.

Re-engineered the Reslicing linear interpolation function for Undirected gradients.  This is in all registrations, 3D and 4D, that use the URAL measure.

Constructing the QuickStart manual for Liver Dual Compartment Dual Input workflow.