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## Watabe Function |

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 Watabe 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 Watabe model applied by Watabe et al [1] for modeling of the parent fraction has the following functional form

with B set to 2. The calculated fraction is multiplied with fp, 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 model 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 Watabe 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.Watabe H, Channing MA, Der MG, Adams HR, Jagoda E, Herscovitch P, Eckelman WC, Carson RE: Kinetic analysis of the 5-HT2A ligand [11C]MDL 100,907. J Cereb Blood Flow Metab 2000, 20(6):899-909. DOI