In some situations the introduction of prior (physiologic) knowledge can help improving the stability of model fitting.
For instance, in receptor experiments it may be adequate to assume that the distribution volume (K1/k2) of the non-displaceable compartment and/or the dissociation rate from specific binding sites (k4) are equal in certain tissues of the brain. Hence, a simultaneous fit of selected regional TACs of a scan can be performed which finds separate K1 and k3 values per TAC, but which delivers a K1/k2 and k4 which is common for all TACs. As an example, Sanabria-Bohorquez et al  have used a coupled k4 for solving the problem of unstable fits. In PKIN this type of fitting is called Coupled Fitting.
Another valuable application of Coupled Fitting is determination of k2' for Reference Tissue models. k2' denotes clearance of the tracer from the reference tissue. Hence, it is natural to enforce a common k2' as physiologic restriction when fitting the TACs from different target tissues as explained below.
The concept can be extended to the fitting of data from different scans of the same subject, for instance test/retest scans which are replicate measurements under the same conditions and where the parameters should be very similar if the regions are consistently outlined. Plisson et al.  have applied simultaneous fitting with the data of pigs which were studied in a baseline condition and with different degrees of receptor blocking by cold compound. By applying the simultaneous fitting, they were able to get stable estimates, which was not possible with independent fitting. In PKIN this type of fitting is called Coupled Studies Fitting and distinguishes two variants of coupling. GLOBAL coupling of a parameter results in single value which is common for all fitted TACs. REGIONAL coupling of a parameter results in common value per region. For instance, if k3 is defined as a parameter with REGIONAL coupling and the coupled regions from two scans are caudate, putamen and frontal, a different k3 estimate will result for each of these three regions, but each of them is common across the TACs of the two scans.
The requirements for coupled fitting in PKIN are:
1.Sanabria-Bohorquez SM, Hamill TG, Goffin K, De Lepeleire I, Bormans G, Burns HD, Van Laere K. Kinetic analysis of the cannabinoid-1 receptor PET tracer [(18)F]MK-9470 in human brain. Eur J Nucl Med Mol Imaging. 2010;37(5):920-33. DOI
2.Plisson C, Gunn RN, Cunningham VJ, Bender D, Salinas CA, Medhurst AD, Roberts JC, Laruelle M, Gee AD. 11C-GSK189254: a selective radioligand for in vivo central nervous system imaging of histamine H3 receptors by PET. J Nucl Med. 2009;50(12):2064-72. DOI