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 **3-Exponential **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 general **3-Exponential **model for the parent fraction has the following functional form

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 as a sum of three exponentials with halftimes T_{1}, T_{2} and T_{3}. Note that the calculated fractions are restricted to the physiologic [0,1] value range.

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**, **Amplitude 1**, **2**, **3** (=A_{1}, A_{2}, A_{3}) and **Halftime 1**, **2**, **3** (=T_{1}, T_{2}, T_{3})**.** All data samples are considered in the fitting process irrespective of **Begin**. The three **Amplitude** parameters are restricted to the range [0,1] per default.

Use without Measured Parent Fraction

The **3-Exponential **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.