Sigmoid Function

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Sigmoid 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 Sigmoid 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 Sigmoid function for the parent fraction has been applied for [11C]PBR28 and has the following functional form [1]


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.


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 A, B and C.

Use without Measured Parent Fraction

The Sigmoid 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.


1.Owen DR, Guo Q, Kalk NJ, Colasanti A, Kalogiannopoulou D, Dimber R, Lewis YL, Libri V, Barletta J, Ramada-Magalhaes J, Kamalakaran A, Nutt DJ, Passchier J, Matthews PM, Gunn RN, Rabiner EA. Determination of [(11)C]PBR28 binding potential in vivo: a first human TSPO blocking study. J Cereb Blood Flow Metab. 2014;34(6):989-94. DOI