Support:Documents:Examples:Estimate Change of Neurotransmitter

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Model of Neurotransmitter PET (ntPET)

Overview

The changes of endogenous neurotransmitter by PET scanning after a stimulus have been proved with different approaches. In stead of detecting the increase or decrease of a neurotransmitter, it is important to characterize the temporal change of a neurotransmitter after a stimulus. Morris proposed the new technique (called ntPET) for capturing the dynamic changes of a neurotransmitter after a stimulus and demonstrated the ability of this method to reconstruct the temporal characteristics of an enhance in neurotransmitter concentration.

Generally, there are two separate injections of tracer for ntPET: one for the rest condition (without any stimuli) and the other for the activation condition (after a stimulus). Therefore, the model can be described as:

Model.jpg

This model can be described by the differential equations:

dF/dt = K1Cp - K2F - Kon[Bmax - B - B2 - Ben]F + koffB

dB/dt = Kon[Bmax - B - B2 - Ben]F - koffB

dF2/dt = K1Cp2 - K2F2 - Kon[Bmax - B - B2 - Ben]F2 + koffB2

dB2/dt = Kon[Bmax - B - B2 - Ben]F2 - koffB2

dBen/dt = Kenon[Bmax - B - B2 - Ben]Fen -kenoffBen


Cp is the plasma concentration of tracer at the first injection (the "rest" condition).

F and B are free (unbound) and bound molar concentrations of tracer after the first injection

Cp2 is the plasma concentration of tracer at the second injection (the "activation" condition).

F2 and B2 are free (unbound) and bound molar concentrations of tracer after the second injection.

Fen and Ben are free and bound molar concentrations of a neurotransmitter released by endogenous ligand after a stimulus.

Bmax is the maximum number of receptors that can be bound by neurotransmitter or tracer.

Bmax - B - B2 - Ben is the concentration of available receptors. This also indicates that binding is saturable.


Implementing the Compartment Model

Create a new model for ntPET