Coupled Fitting

In some situations prior knowledge can help to improve the stability of fitting. 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 different tissues of the brain. Hence, a fit can be performed which finds a separate K₁ and k₃ for each regional TAC, but which delivers a K₁/k₂ and k₄ common across the regions.

In PKIN this task can be achieved with a coupled fit. The requirements are:

• The same kinetic compartment model applies to the TACs of several tissue regions. (non-compartment models may not be coupled).
• There exists one parameter in the model configuration which can be assumed to have the same value in the different tissues, or there is an input curve parameter which should be fitted.

Given these requirements, the user specifies the coupled fit configuration on the Coupled pane:

In the upper section the kinetic model parameters are listed. Check those parameters which are to be coupled among regions. The lower section lists all selectable regional TACs (having the same model). Check all regions which are to be included in coupled fitting.

Fit coupled starts the fitting process as follows:

• A global target curve is created by stacking the TACs of the checked regions (valid points only).
• The corresponding weights are calculated according to the weighting configuration for each TAC.
• A table of fitted parameters is formed by entering the common parameters once and adding all the other fit enabled parameters in the coupled regions. The initial values of common parameters are taken from the first checked region, for the other parameters from the individual regional models. If Fit blood parameters is enabled on the Fitting pane, the fit-enabled parameters of the blood curves are also taken into account.
• The optimizer calculates the model curve in all checked regions, creates the global result curve corresponding to the target curve, weighs all the residuals and forms the global sum of squares as the figure of merit. The parameters are adjusted until the cost function has been minimized, and the resulting parameters are copied back to the individual models.

Note: Coupled fitting may take significant processing time. Thus the Batch mode facility may be a helpful option to run such jobs at less busy times.