The sequential steps for converting blood measurements to an input curve are explained in a dedicated section. The current parent fraction model serves for converting a plasma activity curve into an input curve (authentic, unchanged tracer in plasma).

The **Hill **model assumes that the concentration ratio of authentic tracer to total tracer in plasma has been determined at certain times during the acquisition and loaded with the **Load Fraction** entry in the menu.

Operational Model Curve

The **Hill **model applied by Gunn et al [1] for modeling of the parent fraction has the following functional form

whereby the calculated fraction is multiplied with f_{p}, the free fraction of authentic tracer in plasma, i.e. the fraction of tracer not bound to plasma proteins.

The fraction calculation assumes negligible metabolites before a **Begin **time, and therefore remains constant at 1. From **Begin **on it decreases smoothly.

Parameter Fitting

The free fraction **fp** is an input parameter which has no impact on fitting the **Hill **curve to the fraction data. The default for **fp** is 1 as it is experimentally difficult to measure.

The model supports the fitting of the parameters **Begin**, **A**, **B** and **C.** All data samples are considered in the fitting process irrespective of **Begin**. The scaling parameter **A** is restricted to the range [0,1] per default.

Use without Measured Parent Fraction

The **Hill **parent fraction model can be applied even if no parent fraction measurements were loaded. In this case the user has to specify a parameter set which establishes a representative metabolite correction for the used tracer.

Reference

1. Gunn RN, Sargent PA, Bench CJ, Rabiner EA, Osman S, Pike VW, Hume SP, Grasby PM, Lammertsma AA: Tracer kinetic modeling of the 5-HT1A receptor ligand [carbonyl-11C]WAY-100635 for PET. Neuroimage 1998, 8(4):426-440. DOI